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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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Clemmer JT, Robbins MO. Anisotropic avalanches and critical depinning of three-dimensional magnetic domain walls. Phys Rev E 2019; 100:042121. [PMID: 31770980 DOI: 10.1103/physreve.100.042121] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2019] [Indexed: 11/07/2022]
Abstract
Simulations with more than 10^{12} spins are used to study the motion of a domain wall driven through a three-dimensional random-field Ising magnet (RFIM) by an external field H. The interface advances in a series of avalanches whose size diverges at a critical external field H_{c}. Finite-size scaling is applied to determine critical exponents and test scaling relations. Growth is intrinsically anisotropic with the height of an avalanche normal to the interface ℓ_{⊥} scaling as the width along the interface ℓ_{∥} to a power χ=0.85±0.01. The total interface roughness is consistent with self-affine scaling with a roughness exponent ζ≈χ that is much larger than values found previously for the RFIM and related models that explicitly break orientational symmetry by requiring the interface to be single-valued. Because the RFIM maintains orientational symmetry, the interface develops overhangs that may surround unfavorable regions to create uninvaded bubbles. Overhangs complicate measures of the roughness exponent but decrease in importance with increasing system size.
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Affiliation(s)
- Joel T Clemmer
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
| | - Mark O Robbins
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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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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Bupathy A, Banerjee V, Puri S. Random-field Ising model on isometric lattices: Ground states and non-Porod scattering. Phys Rev E 2016; 93:012104. [PMID: 26871021 DOI: 10.1103/physreve.93.012104] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2015] [Indexed: 11/07/2022]
Abstract
We use a computationally efficient graph cut method to obtain ground state morphologies of the random-field Ising model (RFIM) on (i) simple cubic (SC), (ii) body-centered cubic (BCC), and (iii) face-centered cubic (FCC) lattices. We determine the critical disorder strength Δ_{c} at zero temperature with high accuracy. For the SC lattice, our estimate (Δ_{c}=2.278±0.002) is consistent with earlier reports. For the BCC and FCC lattices, Δ_{c}=3.316±0.002 and 5.160±0.002, respectively, which are the most accurate estimates in the literature to date. The small-r behavior of the correlation function exhibits a cusp regime characterized by a cusp exponent α signifying fractal interfaces. In the paramagnetic phase, α=0.5±0.01 for all three lattices. In the ferromagnetic phase, the cusp exponent shows small variations due to the lattice structure. Consequently, the interfacial energy E_{i}(L) for an interface of size L is significantly different for the three lattices. This has important implications for nonequilibrium properties.
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Affiliation(s)
- Arunkumar Bupathy
- Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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Shrivastav GP, Kumar M, Banerjee V, Puri S. Ground-state morphologies in the random-field Ising model: scaling properties and non-Porod behavior. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032140. [PMID: 25314428 DOI: 10.1103/physreve.90.032140] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2014] [Indexed: 06/04/2023]
Abstract
We use a computationally efficient graph-cut method (GCM) to obtain the ground-state morphologies (at zero temperature) of the random-field Ising model in d=2,3. The GCM enables us to obtain comprehensive numerical results on large-scale systems. We analyze the morphologies by computing correlation functions and structure factors. These quantities enable us to precisely evaluate characteristic properties, e.g., domain sizes, scaling functions, roughness exponents, fractal dimensions, etc.
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Affiliation(s)
- Gaurav P Shrivastav
- Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India and School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Manoj Kumar
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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Roters L, Hucht A, Lübeck S, Nowak U, Usadel KD. Depinning transition and thermal fluctuations in the random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:5202-7. [PMID: 11970390 DOI: 10.1103/physreve.60.5202] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/1999] [Indexed: 04/18/2023]
Abstract
We analyze the depinning transition of a driven interface in the three-dimensional (3D) random field Ising model (RFIM) with quenched disorder by means of Monte Carlo simulations. The interface initially built into the system is perpendicular to the [111] direction of a simple cubic lattice. We introduce an algorithm which is capable of simulating such an interface independent of the considered dimension and time scale. This algorithm is applied to the 3D RFIM to study both the depinning transition and the influence of thermal fluctuations on this transition. It turns out that in the RFIM characteristics of the depinning transition depend crucially on the existence of overhangs. Our analysis yields critical exponents of the interface velocity, the correlation length, and the thermal rounding of the transition. We find numerical evidence for a scaling relation for these exponents and the dimension d of the system.
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Affiliation(s)
- L Roters
- Theoretische Tieftemperaturphysik, Gerhard-Mercator-Universität Duisburg, 47048 Duisburg, Germany.
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Watson J, Fisher DS. Collective particle flow through random media. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:938-954. [PMID: 9985361 DOI: 10.1103/physrevb.54.938] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Dahmen K, Sethna JP. Hysteresis, avalanches, and disorder-induced critical scaling: A renormalization-group approach. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:14872-14905. [PMID: 9983282 DOI: 10.1103/physrevb.53.14872] [Citation(s) in RCA: 201] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Marsili M, Caldarelli G, Vendruscolo M. Quenched disorder, memory, and self-organization. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:R13-R16. [PMID: 9964383 DOI: 10.1103/physreve.53.r13] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Urbach JS, Madison RC, Markert JT. Interface depinning, self-organized criticality, and the Barkhausen effect. PHYSICAL REVIEW LETTERS 1995; 75:276-279. [PMID: 10059653 DOI: 10.1103/physrevlett.75.276] [Citation(s) in RCA: 23] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Nolle CS, Koiller B, Martys N, Robbins MO. Morphology and dynamics of interfaces in random two-dimensional media. PHYSICAL REVIEW LETTERS 1993; 71:2074-2077. [PMID: 10054576 DOI: 10.1103/physrevlett.71.2074] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Ji H, Robbins MO. Percolative, self-affine, and faceted domain growth in random three-dimensional magnets. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:14519-14527. [PMID: 10003553 DOI: 10.1103/physrevb.46.14519] [Citation(s) in RCA: 62] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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