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Spasojević D, Marinković M, Jovković D, Janićević S, Laurson L, Djordjević A. Barkhausen noise in disordered striplike ferromagnets: Experiment versus simulations. Phys Rev E 2024; 109:024110. [PMID: 38491707 DOI: 10.1103/physreve.109.024110] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2023] [Accepted: 01/29/2024] [Indexed: 03/18/2024]
Abstract
In this work, we present a systematic comparison of the results obtained from the low-frequency Barkhausen noise recordings in nanocrystalline samples with those from the numerical simulations of the random-field Ising model systems. We performed measurements at room temperature on a field-driven metallic glass stripe made of VITROPERM 800 R, a nanocrystalline iron-based material with an excellent combination of soft and magnetic properties, making it a cutting-edge material for a wide range of applications. Given that the Barkhausen noise emissions emerging along a hysteresis curve are stochastic and depend in general on a variety of factors (such as distribution of disorder due to impurities or defects, varied size of crystal grains, type of domain structure, driving rate of the external magnetic field, sample shape and temperature, etc.), adequate theoretical modeling is essential for their interpretation and prediction. Here the Random field Ising model, specifically its athermal nonequilibrium version with the finite driving rate, stands out as an appropriate choice due to the material's nanocrystalline structure and high Curie temperature. We performed a systematic analysis of the signal properties and magnetization avalanches comparing the outcomes of the numerical model and experiments carried out in a two-decade-wide range of the external magnetic field driving rates. Our results reveal that with a suitable choice of parameters, a considerable match with the experimental results is achieved, indicating that this model can accurately describe the Barkhausen noise features in nanocrystalline samples.
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Affiliation(s)
- Djordje Spasojević
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Republic of Serbia
| | - Miloš Marinković
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Republic of Serbia
| | - Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, P. O. Box 162, 11000 Belgrade, Republic of Serbia
| | - Sanja Janićević
- Faculty of Science, University of Kragujevac, P. O. Box 60, 34000 Kragujevac, Republic of Serbia
| | - Lasse Laurson
- Computational Physics Laboratory, Tampere University, P. O. Box 692, FI-33014 Tampere, Finland
| | - Antonije Djordjević
- School of Electrical Engineering, University of Belgrade, 11000 Belgrade, Republic of Serbia and Serbian Academy of Sciences and Arts, 11000 Belgrade, Republic of Serbia
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2
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Farkaš LN, Tarjus G, Balog I. Approach to the lower critical dimension of the φ^{4} theory in the derivative expansion of the functional renormalization group. Phys Rev E 2023; 108:054107. [PMID: 38115505 DOI: 10.1103/physreve.108.054107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 10/11/2023] [Indexed: 12/21/2023]
Abstract
We revisit the approach to the lower critical dimension d_{lc} in the Ising-like φ^{4} theory within the functional renormalization group by studying the lowest approximation levels in the derivative expansion of the effective average action. Our goal is to assess how the latter, which provides a generic approximation scheme valid across dimensions and found to be accurate in d≥2, is able to capture the long-distance physics associated with the expected proliferation of localized excitations near d_{lc}. We show that the convergence of the fixed-point effective potential is nonuniform in the field when d→d_{lc} with the emergence of a boundary layer around the minimum of the potential. This allows us to make analytical predictions for the value of the lower critical dimension d_{lc} and for the behavior of the critical temperature as d→d_{lc}, which are both found in fair agreement with the known results. This confirms the versatility of the theoretical approach.
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Affiliation(s)
- Lucija Nora Farkaš
- Department of Physics, University of Zagreb, Bijenička c. 32, 10000 Zagreb, Croatia and LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Place Jussieu, 75252 Paris cedex 05, France
| | - Gilles Tarjus
- LPTMC, CNRS-UMR 7600, Sorbonne Université, 4 Place Jussieu, 75252 Paris cedex 05, France
| | - Ivan Balog
- Institute of Physics, P.O.Box 304, Bijenička cesta 46, HR-10001 Zagreb, Croatia
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3
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Spasojević D, Graovac S, Janićević S. Interplay of disorder and type of driving in disordered ferromagnetic systems. Phys Rev E 2022; 106:044107. [PMID: 36397527 DOI: 10.1103/physreve.106.044107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/18/2022] [Accepted: 09/19/2022] [Indexed: 06/16/2023]
Abstract
We investigate the effects of adiabatic, quasistatic, and finite-rate types of driving on the evolution of disordered three-dimensional ferromagnetic systems, studied within the frame of the nonequilibrium athermal random field Ising model. The effects were examined in all three domains of disorder (low, high, and transitional) for all types of driving, and in a wide range of driving rates for quasistatic and finite-rate driving, providing an extensive overview and comparison of the joint effects that the disorder, type of driving, and rate regime have on the system's behavior.
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Affiliation(s)
- Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Stefan Graovac
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Sanja Janićević
- Faculty of Science, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia
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4
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Wang QH, Bedoya-Pinto A, Blei M, Dismukes AH, Hamo A, Jenkins S, Koperski M, Liu Y, Sun QC, Telford EJ, Kim HH, Augustin M, Vool U, Yin JX, Li LH, Falin A, Dean CR, Casanova F, Evans RFL, Chshiev M, Mishchenko A, Petrovic C, He R, Zhao L, Tsen AW, Gerardot BD, Brotons-Gisbert M, Guguchia Z, Roy X, Tongay S, Wang Z, Hasan MZ, Wrachtrup J, Yacoby A, Fert A, Parkin S, Novoselov KS, Dai P, Balicas L, Santos EJG. The Magnetic Genome of Two-Dimensional van der Waals Materials. ACS NANO 2022; 16:6960-7079. [PMID: 35442017 PMCID: PMC9134533 DOI: 10.1021/acsnano.1c09150] [Citation(s) in RCA: 68] [Impact Index Per Article: 34.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/15/2021] [Accepted: 02/23/2022] [Indexed: 05/23/2023]
Abstract
Magnetism in two-dimensional (2D) van der Waals (vdW) materials has recently emerged as one of the most promising areas in condensed matter research, with many exciting emerging properties and significant potential for applications ranging from topological magnonics to low-power spintronics, quantum computing, and optical communications. In the brief time after their discovery, 2D magnets have blossomed into a rich area for investigation, where fundamental concepts in magnetism are challenged by the behavior of spins that can develop at the single layer limit. However, much effort is still needed in multiple fronts before 2D magnets can be routinely used for practical implementations. In this comprehensive review, prominent authors with expertise in complementary fields of 2D magnetism (i.e., synthesis, device engineering, magneto-optics, imaging, transport, mechanics, spin excitations, and theory and simulations) have joined together to provide a genome of current knowledge and a guideline for future developments in 2D magnetic materials research.
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Affiliation(s)
- Qing Hua Wang
- Materials
Science and Engineering, School for Engineering of Matter, Transport
and Energy, Arizona State University, Tempe, Arizona 85287, United States
| | - Amilcar Bedoya-Pinto
- NISE
Department, Max Planck Institute of Microstructure
Physics, 06120 Halle, Germany
- Instituto
de Ciencia Molecular (ICMol), Universitat
de València, 46980 Paterna, Spain
| | - Mark Blei
- Materials
Science and Engineering, School for Engineering of Matter, Transport
and Energy, Arizona State University, Tempe, Arizona 85287, United States
| | - Avalon H. Dismukes
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
| | - Assaf Hamo
- Department
of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Sarah Jenkins
- Twist
Group,
Faculty of Physics, University of Duisburg-Essen, Campus Duisburg, 47057 Duisburg, Germany
| | - Maciej Koperski
- Institute
for Functional Intelligent Materials, National
University of Singapore, 117544 Singapore
| | - Yu Liu
- Condensed
Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Qi-Chao Sun
- Physikalisches
Institut, University of Stuttgart, 70569 Stuttgart, Germany
| | - Evan J. Telford
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
- Department
of Physics, Columbia University, New York, New York 10027, United States
| | - Hyun Ho Kim
- School
of Materials Science and Engineering, Department of Energy Engineering
Convergence, Kumoh National Institute of
Technology, Gumi 39177, Korea
| | - Mathias Augustin
- Institute
for Condensed Matter Physics and Complex Systems, School of Physics
and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
- Donostia
International Physics Center (DIPC), 20018 Donostia-San Sebastián, Basque Country, Spain
| | - Uri Vool
- Department
of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- John Harvard
Distinguished Science Fellows Program, Harvard
University, Cambridge, Massachusetts 02138, United States
| | - Jia-Xin Yin
- Laboratory
for Topological Quantum Matter and Spectroscopy, Department of Physics, Princeton University, Princeton, New Jersey 08544, United States
| | - Lu Hua Li
- Institute
for Frontier Materials, Deakin University, Geelong Waurn Ponds Campus, Waurn Ponds, Victoria 3216, Australia
| | - Alexey Falin
- Institute
for Frontier Materials, Deakin University, Geelong Waurn Ponds Campus, Waurn Ponds, Victoria 3216, Australia
| | - Cory R. Dean
- Department
of Physics, Columbia University, New York, New York 10027, United States
| | - Fèlix Casanova
- CIC nanoGUNE
BRTA, 20018 Donostia - San Sebastián, Basque
Country, Spain
- IKERBASQUE,
Basque Foundation for Science, 48013 Bilbao, Basque Country, Spain
| | - Richard F. L. Evans
- Department
of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
| | - Mairbek Chshiev
- Université
Grenoble Alpes, CEA, CNRS, Spintec, 38000 Grenoble, France
- Institut
Universitaire de France, 75231 Paris, France
| | - Artem Mishchenko
- Department
of Physics and Astronomy, University of
Manchester, Manchester, M13 9PL, United Kingdom
- National
Graphene Institute, University of Manchester, Manchester, M13 9PL, United Kingdom
| | - Cedomir Petrovic
- Condensed
Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, United States
| | - Rui He
- Department
of Electrical and Computer Engineering, Texas Tech University, 910 Boston Avenue, Lubbock, Texas 79409, United
States
| | - Liuyan Zhao
- Department
of Physics, University of Michigan, 450 Church Street, Ann Arbor, Michigan 48109, United States
| | - Adam W. Tsen
- Institute
for Quantum Computing and Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Brian D. Gerardot
- SUPA, Institute
of Photonics and Quantum Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, United Kingdom
| | - Mauro Brotons-Gisbert
- SUPA, Institute
of Photonics and Quantum Sciences, Heriot-Watt
University, Edinburgh EH14 4AS, United Kingdom
| | - Zurab Guguchia
- Laboratory
for Muon Spin Spectroscopy, Paul Scherrer
Institute, CH-5232 Villigen PSI, Switzerland
| | - Xavier Roy
- Department
of Chemistry, Columbia University, New York, New York 10027, United States
| | - Sefaattin Tongay
- Materials
Science and Engineering, School for Engineering of Matter, Transport
and Energy, Arizona State University, Tempe, Arizona 85287, United States
| | - Ziwei Wang
- Department
of Physics and Astronomy, University of
Manchester, Manchester, M13 9PL, United Kingdom
- National
Graphene Institute, University of Manchester, Manchester, M13 9PL, United Kingdom
| | - M. Zahid Hasan
- Materials
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
- Princeton
Institute for Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, United States
- National
High Magnetic Field Laboratory, Florida
State University, Tallahassee, Florida 32310, United States
| | - Joerg Wrachtrup
- Physikalisches
Institut, University of Stuttgart, 70569 Stuttgart, Germany
- Max Planck
Institute for Solid State Research, 70569 Stuttgart, Germany
| | - Amir Yacoby
- Department
of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- John A.
Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
| | - Albert Fert
- Donostia
International Physics Center (DIPC), 20018 Donostia-San Sebastián, Basque Country, Spain
- Unité
Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
- Department
of Materials Physics UPV/EHU, 20018 Donostia - San Sebastián, Basque Country, Spain
| | - Stuart Parkin
- NISE
Department, Max Planck Institute of Microstructure
Physics, 06120 Halle, Germany
| | - Kostya S. Novoselov
- Institute
for Functional Intelligent Materials, National
University of Singapore, 117544 Singapore
| | - Pengcheng Dai
- Department
of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Luis Balicas
- National
High Magnetic Field Laboratory, Florida
State University, Tallahassee, Florida 32310, United States
- Department
of Physics, Florida State University, Tallahassee, Florida 32306, United States
| | - Elton J. G. Santos
- Institute
for Condensed Matter Physics and Complex Systems, School of Physics
and Astronomy, The University of Edinburgh, Edinburgh, EH9 3FD, United Kingdom
- Donostia
International Physics Center (DIPC), 20018 Donostia-San Sebastián, Basque Country, Spain
- Higgs Centre
for Theoretical Physics, The University
of Edinburgh, Edinburgh EH9 3FD, United Kingdom
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5
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Graovac S, Mijatović S, Spasojević D. Mechanism of subcritical avalanche propagation in three-dimensional disordered systems. Phys Rev E 2021; 103:062123. [PMID: 34271753 DOI: 10.1103/physreve.103.062123] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Accepted: 05/25/2021] [Indexed: 11/07/2022]
Abstract
We present a numerical study on necessary conditions for the appearance of infinite avalanche below the critical point in disordered systems that evolve throughout metastable states. The representative of those systems is the nonequilibrium athermal random-field Ising model. We investigate the impact on propagation of infinite avalanche of both the interface of flipped spins at the avalanche's starting point and the number of independent islands of flipped spins in the system at the moment when the avalanche starts. To deduce what effects are originated due to finite system's size, and to distinguish them from the real necessary conditions for the appearance of the infinite avalanche, we examined lattices of different sizes as well as other key parameters for the avalanche propagation.
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Affiliation(s)
- Stefan Graovac
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
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6
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Jovković D, Janićević S, Mijatović S, Laurson L, Spasojević D. Effects of external noise on threshold-induced correlations in ferromagnetic systems. Phys Rev E 2021; 103:062114. [PMID: 34271613 DOI: 10.1103/physreve.103.062114] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/14/2020] [Accepted: 05/17/2021] [Indexed: 11/07/2022]
Abstract
In the present paper we investigate the impact of the external noise and detection threshold level on the simulation data for the systems that evolve through metastable states. As a representative model of such systems we chose the nonequilibrium athermal random-field Ising model with two types of the external noise, uniform white noise and Gaussian white noise with various different standard deviations, imposed on the original response signal obtained in model simulations. We applied a wide range of detection threshold levels in analysis of the signal and show how these quantities affect the values of exponent γ_{S/T} (describing the scaling of the average avalanche size with duration), the shift of waiting time between the avalanches, and finally the collapses of the waiting time distributions. The results are obtained via extensive numerical simulations on the equilateral three-dimensional cubic lattices of various sizes and disorders.
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Affiliation(s)
- Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, P.O. Box 162, 11000 Belgrade, Serbia
| | - Sanja Janićević
- Faculty of Science, University of Kragujevac, P.O. Box 60, 34000 Kragujevac, Serbia
| | - Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
| | - Lasse Laurson
- Computational Physics Laboratory, Tampere University, P.O. Box 692, FI-33014 Tampere, Finland
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O. Box 44, 11001 Belgrade, Serbia
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7
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Mijatović S, Jovković D, Spasojević D. Nonequilibrium athermal random-field Ising model on hexagonal lattices. Phys Rev E 2021; 103:032147. [PMID: 33862757 DOI: 10.1103/physreve.103.032147] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 03/08/2021] [Indexed: 11/07/2022]
Abstract
We present the results of a study providing numerical evidence for the absence of critical behavior of the nonequilibrium athermal random-field Ising model in adiabatic regime on the hexagonal two-dimensional lattice. The results are obtained on the systems containing up to 32768×32768 spins and are the averages of up to 1700 runs with different random-field configurations per each value of disorder. We analyzed regular systems as well as the systems with different preset conditions to capture behavior in thermodynamic limit. The superficial insight to the avalanche propagation in this type of lattice is given as a stimulus for further research on the topic of avalanche evolution. With obtained data we may conclude that there is no critical behavior of random-field Ising model on hexagonal lattice which is a result that differs from the ones found for the square and for the triangular lattices supporting the recent conjecture that the number of nearest neighbors affects the model criticality.
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Affiliation(s)
- Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P.O.B. 44, 11001 Belgrade, Serbia
| | - Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, P.O.B. 162, 11000 Belgrade, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O.B. 44, 11001 Belgrade, Serbia
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8
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Mijatović S, Branković M, Graovac S, Spasojević D. Avalanche properties in striplike ferromagnetic systems. Phys Rev E 2020; 102:022124. [PMID: 32942372 DOI: 10.1103/physreve.102.022124] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2020] [Accepted: 07/24/2020] [Indexed: 11/07/2022]
Abstract
We present numerical findings on the behavior of the athermal nonequilibrium random-field Ising model of spins at the thin striplike L_{1}×L_{2}×L_{3} cubic lattices with L_{1}<L_{2}<L_{3}. Changing of system sizes highly influences the evolution and shape of avalanches. The smallest avalanches [classified as three-dimension- (3D) like] are unaffected by the system boundaries, the larger are sandwiched between the top and bottom system faces so are 2D-like, while the largest are extended over the system lateral cross section and propagate along the length L_{3} like in 1D systems. Such a structure of avalanches causes double power-law distributions of their size, duration, and energy with larger effective critical exponent corresponding to 3D-like and smaller to 2D-like avalanches. The distributions scale with thickness L_{1} and are collapsible following the proposed scaling predictions which, together with the distributions' shape, might be important for analysis of the Barkhausen noise experimental data for striplike samples. Finally, the impact of system size on external field that triggers the largest avalanche for a given disorder is presented and discussed.
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Affiliation(s)
- Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
| | - Milica Branković
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
| | - Stefan Graovac
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P. O. Box 44, 11001 Belgrade, Serbia
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9
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Mijatović S, Jovković D, Janićević S, Spasojević D. Critical disorder and critical magnetic field of the nonequilibrium athermal random-field Ising model in thin systems. Phys Rev E 2019; 100:032113. [PMID: 31639960 DOI: 10.1103/physreve.100.032113] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2019] [Indexed: 11/07/2022]
Abstract
In the present study of the nonequilibrium athermal random-field Ising model we focus on the behavior of the critical disorder R_{c}(l) and the critical magnetic field H_{c}(l) under different boundary conditions when the system thickness l varies. We propose expressions for R_{c}(l) and H_{c}(l) as well as for the effective critical disorder R_{c}^{eff}(l,L) and effective critical magnetic field H_{c}^{eff}(l,L) playing the role of the effective critical parameters for the L×L×l lattices of finite lateral size L. We support these expressions by the scaling collapses of the magnetization and susceptibility curves obtained in extensive simulations. The collapses are achieved with the two-dimensional (2D) exponents for l below some characteristic value, providing thus a numerical evidence that the thin systems exhibit a 2D-like criticality which should be relevant for the experimental analyses of thin ferromagnetic samples.
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Affiliation(s)
| | - Dragutin Jovković
- Faculty of Mining and Geology, University of Belgrade, POB 162, 11000 Belgrade, Serbia
| | - Sanja Janićević
- Faculty of Science, University of Kragujevac, POB 60, 34000 Kragujevac, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, POB 44, 11001 Belgrade, Serbia
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10
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Thongjaomayum D, Shukla P. Critical hysteresis on dilute triangular lattice. Phys Rev E 2019; 99:062136. [PMID: 31330716 DOI: 10.1103/physreve.99.062136] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2019] [Indexed: 06/10/2023]
Abstract
Critical hysteresis in the zero-temperature random-field Ising model on a two-dimensional triangular lattice was studied earlier with site dilution on one sublattice. It was reported that criticality vanishes if less than one-third of the sublattice is occupied. This appears at variance with recently obtained exact solutions of the model on dilute Bethe lattices and prompts us to revisit the problem using an alternate numerical method. Contrary to our speculation that criticality may not be exactly zero below one-third dilution, the present study indicates it is nearly zero if approximately less than two-thirds of the sublattice is occupied. This suggests that hysteresis on dilute periodic lattices is qualitatively different from that on dilute Bethe lattices. Possible reasons are discussed briefly.
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Affiliation(s)
- Diana Thongjaomayum
- Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon 34051, Republic of Korea
| | - Prabodh Shukla
- Department of Physics, North-Eastern Hill University, Shillong-793022, India
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11
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Tadić B, Mijatović S, Janićević S, Spasojević D, Rodgers GJ. The critical Barkhausen avalanches in thin random-field ferromagnets with an open boundary. Sci Rep 2019; 9:6340. [PMID: 31004121 PMCID: PMC6474887 DOI: 10.1038/s41598-019-42802-w] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2018] [Accepted: 04/04/2019] [Indexed: 11/10/2022] Open
Abstract
The interplay between the critical fluctuations and the sample geometry is investigated numerically using thin random-field ferromagnets exhibiting the field-driven magnetisation reversal on the hysteresis loop. The system is studied along the theoretical critical line in the plane of random-field disorder and thickness. The thickness is varied to consider samples of various geometry between a two-dimensional plane and a complete three-dimensional lattice with an open boundary in the direction of the growing thickness. We perform a multi-fractal analysis of the Barkhausen noise signals and scaling of the critical avalanches of the domain wall motion. Our results reveal that, for sufficiently small thickness, the sample geometry profoundly affects the dynamics by modifying the spectral segments that represent small fluctuations and promoting the time-scale dependent multi-fractality. Meanwhile, the avalanche distributions display two distinct power-law regions, in contrast to those in the two-dimensional limit, and the average avalanche shapes are asymmetric. With increasing thickness, the scaling characteristics and the multi-fractal spectrum in thicker samples gradually approach the hysteresis loop criticality in three-dimensional systems. Thin ferromagnetic films are growing in importance technologically, and our results illustrate some new features of the domain wall dynamics induced by magnetisation reversal in these systems.
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Affiliation(s)
- Bosiljka Tadić
- Department for Theoretical Physics, Jožef Stefan Institute, P.O. Box 3000, SI-1001, Ljubljana, Slovenia. .,Complexity Science Hub, Vienna, Austria.
| | - Svetislav Mijatović
- Faculty of Physics, University of Belgrade, POB 368, 11001, Belgrade, Serbia
| | - Sanja Janićević
- Faculty of Physics, University of Belgrade, POB 368, 11001, Belgrade, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, POB 368, 11001, Belgrade, Serbia
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12
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Abstract
We use Glauber dynamics to study time and temperature dependence of hysteresis in the pure (without quenched disorder) Ising model on cubic, square, honeycomb lattices as well as random graphs. Results are discussed in the context of more extensive studies of hysteresis in the random field Ising model.
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13
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Grassberger P. Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media. PHYSICAL REVIEW LETTERS 2018; 120:200605. [PMID: 29864358 DOI: 10.1103/physrevlett.120.200605] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/12/2017] [Revised: 02/27/2018] [Indexed: 06/08/2023]
Abstract
Based on extensive simulations, we conjecture that critically pinned interfaces in two-dimensional isotropic random media with short-range correlations are always in the universality class of ordinary percolation. Thus, in contrast to interfaces in >2 dimensions, there is no distinction between fractal (i.e., percolative) and rough but nonfractal interfaces. Our claim includes interfaces in zero-temperature random field Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation, and in susceptible-weakened-infected-removed epidemics. It does not include models with long-range correlations in the randomness and models where overhangs are explicitly forbidden (which would imply nonisotropy of the medium).
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14
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Spasojević D, Mijatović S, Navas-Portella V, Vives E. Crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model. Phys Rev E 2018; 97:012109. [PMID: 29448319 DOI: 10.1103/physreve.97.012109] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2017] [Indexed: 11/07/2022]
Abstract
We present extensive numerical studies of the crossover from three-dimensional to two-dimensional systems in the nonequilibrium zero-temperature random-field Ising model with metastable dynamics. Bivariate finite-size scaling hypotheses are presented for systems with sizes L×L×l which explain the size-driven critical crossover from two dimensions (l=const, L→∞) to three dimensions (l∝L→∞). A model of effective critical disorder R_{c}^{eff}(l,L) with a unique fitting parameter and no free parameters in the R_{c}^{eff}(l,L→∞) limit is proposed, together with expressions for the scaling of avalanche distributions bringing important implications for related experimental data analysis, especially in the case of thin three-dimensional systems.
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Affiliation(s)
- Djordje Spasojević
- Faculty of Physics, University of Belgrade, POB 368, 11001 Belgrade, Serbia
| | | | - Víctor Navas-Portella
- Centre de Recerca Matematica, Edifici C, Campus Bellaterra, E-08193 Bellaterra, Catalonia, Spain; Barcelona Graduate School of Mathematics (BGSMath), Edifici C, Campus Bellaterra, E-08193 Barcelona, Spain; and Facultat de Matemàtiques i Informàtica, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, E-08007 Barcelona, Spain
| | - Eduard Vives
- Departament de Matèria Condensada, Facultat de Física, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Catalonia, Spain
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15
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Janićević S, Jovković D, Laurson L, Spasojević D. Threshold-induced correlations in the Random Field Ising Model. Sci Rep 2018; 8:2571. [PMID: 29416055 PMCID: PMC5803239 DOI: 10.1038/s41598-018-20759-6] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/03/2018] [Accepted: 01/22/2018] [Indexed: 11/30/2022] Open
Abstract
We present a numerical study of the correlations in the occurrence times of consecutive crackling noise events in the nonequilibrium zero-temperature Random Field Ising model in three dimensions. The critical behavior of the system is portrayed by the intermittent bursts of activity known as avalanches with scale-invariant properties which are power-law distributed. Our findings, based on the scaling analysis and collapse of data collected in extensive simulations show that the observed correlations emerge upon applying a finite threshold to the pertaining signals when defining events of interest. Such events are called subavalanches and are obtained by separation of original avalanches in the thresholding process. The correlations are evidenced by power law distributed waiting times and are present in the system even when the original avalanche triggerings are described by a random uncorrelated process.
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Affiliation(s)
- Sanja Janićević
- Faculty of Physics, University of Belgrade, POB 368, 11001, Belgrade, Serbia
| | - Dragutin Jovković
- Faculty of Physics, University of Belgrade, POB 368, 11001, Belgrade, Serbia
| | - Lasse Laurson
- COMP Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076, Aalto, Espoo, Finland.
- Helsinki Institute of Physics, Department of Applied Physics, Aalto University, P.O. Box 11100, 00076, Aalto, Espoo, Finland.
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, POB 368, 11001, Belgrade, Serbia
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16
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Janićević S, Mijatović S, Spasojević D. Critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model on a triangular lattice. Phys Rev E 2017; 95:042131. [PMID: 28505865 DOI: 10.1103/physreve.95.042131] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2016] [Indexed: 06/07/2023]
Abstract
We present a numerical study of the critical behavior of the nonequilibrium zero-temperature random field Ising model in two dimensions on a triangular lattice. Our findings, based on the scaling analysis and collapse of data collected in extensive simulations of systems with linear sizes up to L=65536, show that the model is in a different universality class than the same model on a quadratic lattice, which is relevant for a better understanding of model universality and the analysis of experimental data.
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Affiliation(s)
- Sanja Janićević
- Faculty of Physics, University of Belgrade, P.O. Box 368, 11001 Belgrade, Serbia
| | - Svetislav Mijatović
- Faculty of Physics, University of Belgrade, P.O. Box 368, 11001 Belgrade, Serbia
| | - Djordje Spasojević
- Faculty of Physics, University of Belgrade, P.O. Box 368, 11001 Belgrade, Serbia
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17
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Shukla P, Thongjaomayum D. Criteria for infinite avalanches in the zero-temperature nonequilibrium random-field Ising model on a Bethe lattice. Phys Rev E 2017; 95:042109. [PMID: 28505775 DOI: 10.1103/physreve.95.042109] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2016] [Indexed: 06/07/2023]
Abstract
We present general criteria for the occurrence of infinite avalanches and critical hysteresis in the zero-temperature nonequilibrium random-field Ising model on a Bethe lattice. Drawing upon extant results as well as a result on a dilute four-coordinated (z=4) lattice, we show that diverging avalanches can occur if an arbitrarily small fraction of sites on a spanning cluster have connectivity z≥4.
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Affiliation(s)
- Prabodh Shukla
- Physics Department, North Eastern Hill University, Shillong-793 022, India
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18
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Chern GW. Magnetic avalanches in granular ferromagnets: thermal activated collective behavior. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:044004. [PMID: 27897133 DOI: 10.1088/1361-648x/29/4/044004] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We present a numerical study on the thermal activated avalanche dynamics in granular materials composed of ferromagnetic clusters embedded in a non-magnetic matrix. A microscopic dynamical simulation based on the reaction-diffusion process is developed to model the magnetization process of such systems. The large-scale simulations presented here explicitly demonstrate inter-granular collective behavior induced by thermal activation of spin tunneling. In particular, we observe an intriguing criticality controlled by the rate of energy dissipation. We show that thermal activated avalanches can be understood in the framework of continuum percolation and the emergent dissipation induced criticality is in the universality class of 3D percolation transition. Implications of these results to the phase-separated states of colossal magnetoresistance materials and other artificial granular magnetic systems are also discussed.
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Navas-Portella V, Vives E. Influence of the aspect ratio and boundary conditions on universal finite-size scaling functions in the athermal metastable two-dimensional random field Ising model. Phys Rev E 2016; 93:022129. [PMID: 26986310 DOI: 10.1103/physreve.93.022129] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2015] [Indexed: 11/07/2022]
Abstract
This work studies universal finite size scaling functions for the number of one-dimensional spanning avalanches in a two-dimensional (2D) disordered system with boundary conditions of different nature and different aspect ratios. To this end, we will consider the 2D random field Ising model at T=0 driven by the external field H with athermal dynamics implemented with periodic and forced boundary conditions. We have chosen a convenient scaling variable z that accounts for the deformation of the distance to the critical point caused by the aspect ratio. In addition, assuming that the dependence of the finite size scaling functions on the aspect ratio can be accounted for by an additional multiplicative factor, we have been able to collapse data for different system sizes, different aspect ratios, and different types of the boundary conditions into a single scaling function Q̂.
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Affiliation(s)
- Víctor Navas-Portella
- Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Catalonia, Spain.,Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, E-08193 Bellaterra, Catalonia, Spain
| | - Eduard Vives
- Departament d'Estructura i Constituents de la Matèria, Facultat de Física, Universitat de Barcelona, Diagonal 645, 08028 Barcelona, Catalonia, Spain
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20
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Kurbah L, Thongjaomayum D, Shukla P. Nonequilibrium random-field Ising model on a diluted triangular lattice. Phys Rev E 2015; 91:012131. [PMID: 25679594 DOI: 10.1103/physreve.91.012131] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/30/2013] [Indexed: 11/07/2022]
Abstract
We study critical hysteresis in the random-field Ising model on a two-dimensional periodic lattice with a variable coordination number z(eff) in the range 3≤z(eff)≤6. We find that the model supports critical behavior in the range 4<z(eff)≤6, but the critical exponents are independent of z(eff). The result is discussed in the context of the universality of nonequilibrium critical phenomena and extant results in the field.
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Affiliation(s)
- Lobisor Kurbah
- Physics Department, North Eastern Hill University, Shillong-793 022, India
| | | | - Prabodh Shukla
- Physics Department, North Eastern Hill University, Shillong-793 022, India
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21
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Mandal PK, Sinha S. Characterization of kinetic coarsening in a random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:042144. [PMID: 24827229 DOI: 10.1103/physreve.89.042144] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2013] [Indexed: 06/03/2023]
Abstract
We report a study of nonequilibrium relaxation in a two-dimensional random field Ising model at a nonzero temperature. We attempt to observe the coarsening from a different perspective with a particular focus on three dynamical quantities that characterize the kinetic coarsening. We provide a simple generalized scaling relation of coarsening supported by numerical results. The excellent data collapse of the dynamical quantities justifies our proposition. The scaling relation corroborates the recent observation that the average linear domain size satisfies different scaling behavior in different time regimes.
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Affiliation(s)
- Pradipta Kumar Mandal
- Department of Physics, Scottish Church College, 1 & 3 Urquhart Square Kolkata 700 006, India
| | - Suman Sinha
- Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700 009, India
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22
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Spasojević D, Janićević S, Knežević M. Analysis of spanning avalanches in the two-dimensional nonequilibrium zero-temperature random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:012118. [PMID: 24580183 DOI: 10.1103/physreve.89.012118] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2013] [Indexed: 06/03/2023]
Abstract
We present a numerical analysis of spanning avalanches in a two-dimensional (2D) nonequilibrium zero-temperature random field Ising model. Finite-size scaling analysis, performed for distribution of the average number of spanning avalanches per single run, spanning avalanche size distribution, average size of spanning avalanche, and contribution of spanning avalanches to magnetization jump, is augmented by analysis of spanning field (i.e., field triggering spanning avalanche), which enabled us to collapse averaged magnetization curves below critical disorder. Our study, based on extensive simulations of sufficiently large systems, reveals the dominant role of subcritical 2D-spanning avalanches in model behavior below and at the critical disorder. Other types of avalanches influence finite systems, but their contribution for large systems remains small or vanish.
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Affiliation(s)
- Djordje Spasojević
- University of Belgrade, Faculty of Physics, POB 44, 11001 Belgrade, Serbia
| | - Sanja Janićević
- University of Belgrade, Faculty of Physics, POB 44, 11001 Belgrade, Serbia
| | - Milan Knežević
- University of Belgrade, Faculty of Physics, POB 44, 11001 Belgrade, Serbia
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23
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Thongjaomayum D, Shukla P. Effect of coordination number on the nonequilibrium critical point. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042138. [PMID: 24229146 DOI: 10.1103/physreve.88.042138] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/16/2013] [Revised: 06/10/2013] [Indexed: 06/02/2023]
Abstract
We study the nonequilibrium critical point of the zero-temperature random-field Ising model on a triangular lattice and compare it with known results on honeycomb, square, and simple cubic lattices. We suggest that the coordination number of the lattice rather than its dimension plays the key role in determining the universality class of the nonequilibrium critical behavior. This is discussed in the context of numerical evidence that equilibrium and nonequilibrium critical points of the zero-temperature random-field Ising model belong to the same universality class. The physics of this curious result is not fully understood.
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Affiliation(s)
- Diana Thongjaomayum
- Department of Physics, North Eastern Hill University, Shillong 793 022, India
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24
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Handford TP, Pérez-Reche FJ, Taraskin SN. Zero-temperature random-field Ising model on a bilayered Bethe lattice. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022117. [PMID: 24032785 DOI: 10.1103/physreve.88.022117] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2013] [Indexed: 06/02/2023]
Abstract
The zero-temperature random-field Ising model is solved analytically for magnetization versus external field for a bilayered Bethe lattice. The mechanisms of infinite avalanches which are observed for small values of disorder are established. The effects of variable interlayer interaction strengths on infinite avalanches are investigated. The spin-field correlation length is calculated and its critical behavior is discussed. Direct Monte Carlo simulations of spin-flip dynamics are shown to support the analytical findings. We find, paradoxically, that a reduction of the interlayer bond strength can cause a phase transition from a regime with continuous magnetization reversal to a regime where magnetization exhibits a discontinuity associated with an infinite avalanche. This effect is understood in terms of the proposed mechanisms for the infinite avalanche.
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Affiliation(s)
- Thomas P Handford
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom
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25
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Handford TP, Pérez-Reche FJ, Taraskin SN. Mechanisms of evolution of avalanches in regular graphs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062122. [PMID: 23848642 DOI: 10.1103/physreve.87.062122] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2013] [Indexed: 06/02/2023]
Abstract
A mapping of avalanches occurring in the zero-temperature random-field Ising model to life periods of a population experiencing immigration is established. Such a mapping allows the microscopic criteria for the occurrence of an infinite avalanche in a q-regular graph to be determined. A key factor for an avalanche of spin flips to become infinite is that it interacts in an optimal way with previously flipped spins. Based on these criteria, we explain why an infinite avalanche can occur in q-regular graphs only for q>3 and suggest that this criterion might be relevant for other systems. The generating function techniques developed for branching processes are applied to obtain analytical expressions for the durations, pulse shapes, and power spectra of the avalanches. The results show that only very long avalanches exhibit a significant degree of universality.
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Affiliation(s)
- Thomas P Handford
- Department of Chemistry, University of Cambridge, Cambridge, United Kingdom.
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Sinha S, Mandal PK. Dynamical properties of random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:022121. [PMID: 23496474 DOI: 10.1103/physreve.87.022121] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/22/2012] [Indexed: 06/01/2023]
Abstract
Extensive Monte Carlo simulations are performed on a two-dimensional random field Ising model. The purpose of the present work is to study the disorder-induced changes in the properties of disordered spin systems. The time evolution of the domain growth, the order parameter, and the spin-spin correlation functions are studied in the nonequilibrium regime. The dynamical evolution of the order parameter and the domain growth shows a power law scaling with disorder-dependent exponents. It is observed that for weak random fields, the two-dimensional random field Ising model possesses long-range order. Except for weak disorder, exchange interaction never wins over pinning interaction to establish long-range order in the system.
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Affiliation(s)
- Suman Sinha
- Department of Physics, University of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata 700009, India.
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27
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Manchanda K, Yadav AC, Ramaswamy R. Scaling behavior in probabilistic neuronal cellular automata. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012704. [PMID: 23410356 DOI: 10.1103/physreve.87.012704] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2012] [Revised: 11/16/2012] [Indexed: 06/01/2023]
Abstract
We study a neural network model of interacting stochastic discrete two-state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective temperature). There are avalanches of neuronal activity, namely, spatially and temporally contiguous sites of activity; a detailed numerical study of these activity avalanches is presented, and single, joint, and marginal probability distributions are computed. At the critical point, we find that the scaling exponents for the variables are in good agreement with a mean-field theory.
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Affiliation(s)
- Kaustubh Manchanda
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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28
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Spasojević D, Janićević S, Knežević M. Avalanche distributions in the two-dimensional nonequilibrium zero-temperature random field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 84:051119. [PMID: 22181381 DOI: 10.1103/physreve.84.051119] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2011] [Indexed: 05/31/2023]
Abstract
We present in detail the scaling analysis and data collapse of avalanche distributions and joint distributions that characterize the recently evidenced critical behavior of the two-dimensional nonequilibrium zero-temperature random field Ising model. The distributions are collected in extensive simulations of systems with linear sizes up to L=131072.
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