1
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Mondal PS, Mishra PK, Mishra S. Ordering kinetics and steady states of XY-model with ferromagnetic and nematic interaction. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:285101. [PMID: 38574681 DOI: 10.1088/1361-648x/ad3abe] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 04/04/2024] [Indexed: 04/06/2024]
Abstract
Previous studies on the generalized XY model have concentrated on the equilibrium phase diagram and the equilibrium nature of distinct phases under varying parameter conditions. We direct our attention towards examining the system's evolution towards equilibrium states across different parameter values, specifically by varying the relative strengths of ferromagnetic and nematic interactions. We study the kinetics of the system, using the temporal annihilation of defects at varying temperatures and its impact on the coarsening behavior of the system. For both pure polar and pure nematic systems, we observe temperature-dependent decay of the exponent, leading to a decelerated growth of domains within the system. At parameter values where both ferromagnetic and nematic interactions are simultaneously present, we show a phase diagram highlighting three low-temperature phases-polar, nematic, and coexistence-along- side a high-temperature disordered phase. Our study provides valuable insights into the complex interplay of interactions, offering a comprehensive understanding of the system's behavior during its evolution towards equilibrium.
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Affiliation(s)
| | | | - Shradha Mishra
- Indian Institute of Technology (BHU), Varanasi 221005, India
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2
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Bhattacharyya R, Sen Gupta B. Kinetics of phase separation and aging dynamics of segregating fluid mixtures in the presence of quenched disorder. SOFT MATTER 2024; 20:2969-2977. [PMID: 38470361 DOI: 10.1039/d4sm00204k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/13/2024]
Abstract
Quenched or frozen-in structural disorder is ubiquitous in real experimental systems. Much of the progress is achieved in understanding the phase separation of such systems using the diffusion-driven coarsening in an Ising model with quenched disorder. But there is a paucity of research on the phase-separation kinetics in fluids with quenched disorder. In this paper, we present results from a detailed molecular dynamics simulation, showing the effects of randomly placed localized impurities on the phase separation kinetics of binary fluid mixtures. Two different models are offered for representing the impurities. We observe a dramatic slowing down in the pattern formation with increasing impurity concentration. This sluggish domain growth kinetics follows a power-law with a disorder-dependent exponent. The correlation function and structure factor show a non-Porod behavior, indicating the roughening of the domain interfaces. We have also studied the effect of quenched disorder on the aging dynamics by calculating the two-time order parameter auto correlation function and find that the Fisher and Huse scaling law holds good in the presence of quenched disorder.
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Affiliation(s)
- Rounak Bhattacharyya
- Institute for Theoretical Physics and BioQuant, Heidelberg University, Heidelberg 69120, Germany
| | - Bhaskar Sen Gupta
- Department of Physics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India.
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3
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Bhandari P, Malik V, Puri S. Phase-ordering kinetics of the asymmetric Coulomb glass model. Phys Rev E 2024; 109:014135. [PMID: 38366509 DOI: 10.1103/physreve.109.014135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 01/03/2024] [Indexed: 02/18/2024]
Abstract
We present results for phase-ordering kinetics in the Coulomb glass (CG) model, which describes electrons on a lattice with unscreened Coulombic repulsion. The filling factor is denoted by K∈[0,1]. For a square lattice with K=0.5 (symmetric CG), the ground state is a checkerboard with alternating electrons and holes. In this paper, we focus on the asymmetric CG where K≲0.5, i.e., the ground state is checkerboard-like with excess holes distributed uniformly. There is no explicit quenched disorder in our system, though the Coulombic interaction gives rise to frustration. We find that the evolution morphology is in the same dynamical universality class as the ordering ferromagnet. Further, the domain growth law is slightly slower than the Lifshitz-Cahn-Allen law, L(t)∼t^{1/2}, i.e., the growth exponent is underestimated. We speculate that this could be a signature of logarithmic growth in the asymptotic regime.
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Affiliation(s)
- Preeti Bhandari
- Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Vikas Malik
- Department of Physics and Material Science, Jaypee Institute of Information Technology, Uttar Pradesh 201309, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India
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4
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Bhattacharyya R, Gupta BS. Effect of annealed disorder on phase separation kinetics and aging phenomena in fluid mixtures. Phys Rev E 2021; 104:054612. [PMID: 34942791 DOI: 10.1103/physreve.104.054612] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2021] [Accepted: 11/03/2021] [Indexed: 11/07/2022]
Abstract
We use state-of-the-art molecular dynamics simulations to study the effects of annealed disorder on the phase-separating kinetics and aging phenomena of a segregating binary fluid mixture. In the presence of disorder, we observe a dramatic slowing down in the phase separation dynamics. The domain growth follows the power law with a disorder-dependent exponent. Due to the energetically favorable positions, the domain boundary roughens, which modifies the correlation function and structure factor to a non-Porod behavior. The correlation function and structure factor provide clear evidence that superuniversality does not hold in our system. The role of annealed disorder on the nonequilibrium aging dynamics is studied qualitatively by computing the two-time order-parameter autocorrelation function. The decay of the correlation function slows down significantly with the disorder. This quantity exhibits scaling laws with respect to the ratio of the domain length at the observation time and the age of the system. We find the scaling laws hold good for the disordered system and are therefore robust and generic to such segregating fluid mixtures.
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Affiliation(s)
- Rounak Bhattacharyya
- Department of Physics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India
| | - Bhaskar Sen Gupta
- Department of Physics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India
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5
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Agrawal R, Kumar M, Puri S. Domain growth and aging in the random field XY model: A Monte Carlo study. Phys Rev E 2021; 104:044123. [PMID: 34781454 DOI: 10.1103/physreve.104.044123] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2021] [Accepted: 10/01/2021] [Indexed: 11/07/2022]
Abstract
We use large-scale Monte Carlo simulations to obtain comprehensive results for domain growth and aging in the random field XY model in dimensions d=2,3. After a deep quench from the paramagnetic phase, the system orders locally via annihilation of topological defects, i.e., vortices and antivortices. The evolution morphology of the system is characterized by the correlation function and the structure factor of the magnetization field. We find that these quantities obey dynamical scaling, and their scaling function is independent of the disorder strength Δ. However, the scaling form of the autocorrelation function is found to be dependent on Δ, i.e., superuniversality is violated. The large-t behavior of the autocorrelation function is explored by studying aging and autocorrelation exponents. We also investigate the characteristic growth law L(t,Δ) in d=2,3, which shows an asymptotic logarithmic behavior: L(t,Δ)∼Δ^{-φ}(lnt)^{1/ψ}, with exponents φ,ψ>0.
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Affiliation(s)
- Ramgopal Agrawal
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Manoj Kumar
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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6
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Enninful HRNB, Schneider D, Enke D, Valiullin R. Impact of Geometrical Disorder on Phase Equilibria of Fluids and Solids Confined in Mesoporous Materials. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2021; 37:3521-3537. [PMID: 33724041 DOI: 10.1021/acs.langmuir.0c03047] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Porous solids used in practical applications often possess structural disorder over broad length scales. This disorder strongly affects different properties of the substances confined in their pore spaces. Quantifying structural disorder and correlating it with the physical properties of confined matter is thus a necessary step toward the rational use of porous solids in practical applications and process optimization. The present work focuses on recent advances made in the understanding of correlations between the phase state and geometric disorder in nanoporous solids. We overview the recently developed statistical theory for phase transitions in a minimalistic model of disordered pore networks: linear chains of pores with statistical disorder. By correlating its predictions with various experimental observations, we show that this model gives notable insight into collective phenomena in phase-transition processes in disordered materials and is capable of explaining self-consistently the majority of the experimental results obtained for gas-liquid and solid-liquid equilibria in mesoporous solids. The potentials of the theory for improving the gas sorption and thermoporometry characterization of porous materials are discussed.
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Affiliation(s)
- Henry R N B Enninful
- Felix Bloch Institute for Solid State Physics, Leipzig University, Linnéstr. 5, 04103 Leipzig, Germany
| | - Daniel Schneider
- Felix Bloch Institute for Solid State Physics, Leipzig University, Linnéstr. 5, 04103 Leipzig, Germany
| | - Dirk Enke
- Institute of Chemical Technology, Leipzig University, Linnéstr. 3, 04103 Leipzig, Germany
| | - Rustem Valiullin
- Felix Bloch Institute for Solid State Physics, Leipzig University, Linnéstr. 5, 04103 Leipzig, Germany
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7
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Vats A, Banerjee V, Puri S. Domain growth in ferronematics: slaved coarsening, emergent morphologies and growth laws. SOFT MATTER 2021; 17:2659-2674. [PMID: 33533368 DOI: 10.1039/d0sm01888k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Ferronematics (FNs) are suspensions of magnetic nanoparticles in nematic liquid crystals (NLCs). They have attracted much experimental attention, and are of great interest both scientifically and technologically. There are very few theoretical studies of FNs, even in equilibrium. In this paper, we study the non-equilibrium phenomenon of domain growth after a thermal quench (or coarsening) in this coupled system. Our modeling is based on coupled time-dependent Ginzburg-Landau (TDGL) equations for two order parameters: the LC tensor order parameter Q, and the magnetization M. We consider both shallow and deep quenches from a high-temperature disordered phase. The system coarsens by the collision and annihilation of topological defects. We focus on slaved coarsening, where a disordered Q (or M) field is driven to coarsen by an ordered M (or Q) field. We present detailed results for the morphologies and growth laws, which exhibit unusual features purely due to the magneto-nematic coupling. To the best of our knowledge, this is the first study of non-equilibrium phenomena in FNs.
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Affiliation(s)
- Aditya Vats
- Department of Physics, Indian Institute of Technology Delhi, New Delhi - 110016, India
| | - Varsha Banerjee
- Department of Physics, Indian Institute of Technology Delhi, New Delhi - 110016, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi - 110067, India.
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8
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Ghosh S, Mukherjee A, Arroyave R, Douglas JF. Impact of particle arrays on phase separation composition patterns. J Chem Phys 2020; 152:224902. [PMID: 32534548 DOI: 10.1063/5.0007859] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We examine the symmetry-breaking effect of fixed constellations of particles on the surface-directed spinodal decomposition of binary blends in the presence of particles whose surfaces have a preferential affinity for one of the components. Our phase-field simulations indicate that the phase separation morphology in the presence of particle arrays can be tuned to have a continuous, droplet, lamellar, or hybrid morphology depending on the interparticle spacing, blend composition, and time. In particular, when the interparticle spacing is large compared to the spinodal wavelength, a transient target pattern composed of alternate rings of preferred and non-preferred phases emerges at early times, tending to adopt the symmetry of the particle configuration. We reveal that such target patterns stabilize for certain characteristic length, time, and composition scales characteristic of the pure phase-separating mixture. To illustrate the general range of phenomena exhibited by mixture-particle systems, we simulate the effects of single-particle, multi-particle, and cluster-particle systems having multiple geometrical configurations of the particle characteristic of pattern substrates on phase separation. Our simulations show that tailoring the particle configuration, or substrate pattern configuration, a relative fluid-particle composition should allow the desirable control of the phase separation morphology as in block copolymer materials, but where the scales accessible to this approach of organizing phase-separated fluids usually are significantly larger. Limited experiments confirm the trends observed in our simulations, which should provide some guidance in engineering patterned blend and other mixtures of technological interest.
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Affiliation(s)
- Supriyo Ghosh
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Arnab Mukherjee
- Center for Hierarchical Materials Design, Northwestern University, Evanston, Illinois 60208, USA
| | - Raymundo Arroyave
- Materials Science and Engineering Department, Texas A&M University, College Station, Texas 77843, USA
| | - Jack F Douglas
- Materials Science and Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
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9
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Kumar A, Narayanam C, Khanna R, Puri S. Slow coarsening in unstable liquid films under gravity on a disordered substrate. Phys Rev E 2020; 101:042801. [PMID: 32422816 DOI: 10.1103/physreve.101.042801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2019] [Accepted: 03/11/2020] [Indexed: 11/07/2022]
Abstract
We study the evolution of unstable liquid films via numerical solutions of the thin-film equation. The film is placed on a coated substrate with disorder. This is modeled by a random spatial variation of the relative value of the Hamaker constants for the substrate and coating. The free energy consists of (a) the van der Waals term for the substrate/coating interactions with the film and (b) a term due to gravity. This free energy admits a Maxwell double-tangent construction with two coexisting phases, i.e., "thin" and "thick" phases. In the absence of disorder, the film dewets by true morphological phase separation (MPS), i.e., the elimination of domain walls between the coexisting phases. The introduction of disorder may result in the trapping of these domain walls, with a drastic slowdown in growth kinetics. We present detailed numerical results in D=2 and D=3 to understand this slow coarsening, where D is the dimensionality of the liquid-film system.
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Affiliation(s)
- Avanish Kumar
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Chaitanya Narayanam
- Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
| | - Rajesh Khanna
- Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi 110016, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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10
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Chatterjee S, Sutradhar S, Puri S, Paul R. Ordering kinetics in a q-state random-bond clock model: Role of vortices and interfaces. Phys Rev E 2020; 101:032128. [PMID: 32290025 DOI: 10.1103/physreve.101.032128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2019] [Accepted: 03/02/2020] [Indexed: 11/07/2022]
Abstract
In this article, we present a Monte Carlo study of phase transition and coarsening dynamics in the nonconserved two-dimensional random-bond q-state clock model (RBCM) deriving from a pure clock model [Chatterjee et al., Phys. Rev. E 98, 032109 (2018)10.1103/PhysRevE.98.032109]. Akin to the pure clock model, RBCM also passes through two different phases when quenched from a disordered initial configuration representing at infinite temperature. Our investigation of the equilibrium phase transition affirms that both upper (T_{c}^{1}) and lower (T_{c}^{2}) phase transition temperatures decrease with bond randomness strength ε. Effect of ε on the nonequilibrium coarsening dynamics is investigated following independent rapid quenches in the quasi-long-range ordered (QLRO, T_{c}^{2}<T<T_{c}^{1}) regime and long-range ordered (LRO, T<T_{c}^{2}) regime at temperature T. We report that the dynamical scaling of the correlation function and structure factor is independent of ε and the presence of quenched disorder slows down domain coarsening. Coarsening dynamics in both LRO and QLRO regimes are further characterized by power-law growth with disorder-dependent exponents within our simulation timescales. The growth exponents in the LRO regime decrease from 0.5 in the pure case to 0.22 in the maximum disordered case, whereas the corresponding change in the QLRO regime happens from 0.45 to 0.38. We further explored the coarsening dynamics in the bond-diluted clock model and, in both the models, the effect of the disorder is more significant for the quench in the LRO regime compared to the QLRO regime.
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Affiliation(s)
- Swarnajit Chatterjee
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India
| | | | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Raja Paul
- School of Mathematical & Computational Sciences, Indian Association for the Cultivation of Science, Kolkata 700032, India
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11
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Bhandari P, Malik V, Puri S. Logarithmic coarsening in the Coulomb glass. Phys Rev E 2019; 99:052113. [PMID: 31212506 DOI: 10.1103/physreve.99.052113] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2019] [Indexed: 11/07/2022]
Abstract
We present numerical results from a comprehensive Monte Carlo study in two dimensions (d=2) of coarsening kinetics in the Coulomb glass (CG) model at half-filling. The CG model is characterized by spin-spin interactions which are long-range Coulombic and antiferromagnetic. For the nonequilibrium properties studied by us (spatial correlation functions and domain growth laws), we find that domain growth in the CG is analogous to that in the nearest-neighbor random-field Ising model. The domain length scale L(t) shows a crossover from a regime of "power-law growth with a disorder-dependent exponent" [L(t)∼t^{1/z[over ¯]}] to a regime of "logarithmic growth with a universal exponent" [L(t)∼(lnt)^{1/ψ}].
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Affiliation(s)
- Preeti Bhandari
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.,Department of Physical Sciences, Indian Institute of Science Education and Research, Mohali 140306, India
| | - Vikas Malik
- Department of Physics and Material Science, Jaypee Institute of Information Technology, Uttar Pradesh 201309, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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12
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Kumar M, Chatterjee S, Paul R, Puri S. Ordering kinetics in the random-bond XY model. Phys Rev E 2018; 96:042127. [PMID: 29347537 DOI: 10.1103/physreve.96.042127] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2017] [Indexed: 11/07/2022]
Abstract
We present a comprehensive Monte Carlo study of domain growth in the random-bond XY model with nonconserved kinetics. The presence of quenched disorder slows down domain growth in d=2,3. In d=2, we observe power-law growth with a disorder-dependent exponent on the time scales of our simulation. In d=3, we see the signature of an asymptotically logarithmic growth regime. The scaling functions for the real-space correlation function are seen to be independent of the disorder. However, the same does not apply for the two-time autocorrelation function, demonstrating the breakdown of superuniversality.
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Affiliation(s)
- M Kumar
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India
| | - S Chatterjee
- Indian Association for the Cultivation of Science, Kolkata-700032, India
| | - R Paul
- Indian Association for the Cultivation of Science, Kolkata-700032, India
| | - S Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India
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13
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Das P, Saha-Dasgupta T, Puri S. Universality of domain growth in antiferromagnets with spin-exchange kinetics. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2017; 40:94. [PMID: 29110108 DOI: 10.1140/epje/i2017-11583-7] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2017] [Accepted: 10/23/2017] [Indexed: 06/07/2023]
Abstract
We study phase ordering kinetics in symmetric and asymmetric binary mixtures, undergoing an order-disorder transition below the critical temperature. Microscopically, we model the kinetics via the antiferromagnetic Ising model with Kawasaki spin-exchange kinetics. This conserves the composition while the order parameter (staggered magnetization) is not conserved. The order-parameter correlation function and structure factor show dynamical scaling, and the scaling functions are independent of the mixture composition. The average domain size shows a power-law growth: [Formula: see text]. The asymptotic growth regime has [Formula: see text], though there can be prolonged transients with [Formula: see text] for asymmetric mixtures. Our unambiguous observation of the asymptotic universal regime is facilitated by using an accelerated Monte Carlo technique. We also obtain the coarse-grained free energy from the Hamiltonian, as a function of two order parameters. The evolution of these order parameters is modeled by using Model C kinetics. As for the microscopic dynamics, the average domain size of the nonconserved order-parameter (staggered magnetization) field exhibits a power-law growth: [Formula: see text] at later times, irrespective of the mean value of the conserved order-parameter (composition) field.
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Affiliation(s)
- Prasenjit Das
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India
| | | | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, India.
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14
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Singh A, Singh A, Chakraborti A. Effect of bond-disorder on the phase-separation kinetics of binary mixtures: A Monte Carlo simulation study. J Chem Phys 2017; 147:124902. [PMID: 28964037 DOI: 10.1063/1.5004563] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present Monte Carlo (MC) simulation studies of phase separation in binary (AB) mixtures with bond-disorder that is introduced in two different ways: (i) at randomly selected lattice sites and (ii) at regularly selected sites. The Ising model with spin exchange (Kawasaki) dynamics represents the segregation kinetics in conserved binary mixtures. We find that the dynamical scaling changes significantly by varying the number of disordered sites in the case where bond-disorder is introduced at the randomly selected sites. On the other hand, when we introduce the bond-disorder in a regular fashion, the system follows the dynamical scaling for the modest number of disordered sites. For a higher number of disordered sites, the evolution morphology illustrates a lamellar pattern formation. Our MC results are consistent with the Lifshitz-Slyozov power-law growth in all the cases.
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Affiliation(s)
- Awaneesh Singh
- Department of Physics, Institute of Chemical Technology, Mumbai 400019, India
| | - Amrita Singh
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Anirban Chakraborti
- School of Computational and Integrative Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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15
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Christiansen H, Majumder S, Janke W. Coarsening and aging of lattice polymers: Influence of bond fluctuations. J Chem Phys 2017; 147:094902. [DOI: 10.1063/1.4991667] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, Postfach 100 920, 04009 Leipzig, Germany
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16
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Corberi F, Kumar M, Puri S, Lippiello E. Equilibrium structure and off-equilibrium kinetics of a magnet with tunable frustration. Phys Rev E 2017; 95:062136. [PMID: 28709286 DOI: 10.1103/physreve.95.062136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2017] [Indexed: 06/07/2023]
Abstract
We study numerically a two-dimensional random-bond Ising model where frustration can be tuned by varying the fraction a of antiferromagnetic coupling constants. At low temperatures the model exhibits a phase with ferromagnetic order for sufficiently small values of a, a<a_{f}. In an intermediate range, a_{f}<a<a_{a}, the system is paramagnetic, with spin-glass order expected right at zero temperature. For even larger values, a>a_{a}, an antiferromagnetic phase exists. After a deep quench from high temperatures, slow evolution is observed for any value of a. We show that different amounts of frustration, tuned by a, affect the dynamical properties in a highly nontrivial way. In particular, the kinetics is logarithmically slow in phases with ferromagnetic or antiferromagnetic order, whereas evolution is faster, i.e., algebraic, when spin-glass order is prevailing. An interpretation is given in terms of the different nature of phase space.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Fisica "E.R. Caianiello", and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
| | - Manoj Kumar
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Eugenio Lippiello
- Dipartimento di Matematica e Fisica, University of Campania "L. Vanvitelli", viale Lincoln, 5 81100 Caserta, Italy
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17
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Corberi F, Cugliandolo LF, Insalata F, Picco M. Coarsening and percolation in a disordered ferromagnet. Phys Rev E 2017; 95:022101. [PMID: 28297910 DOI: 10.1103/physreve.95.022101] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2016] [Indexed: 06/06/2023]
Abstract
By studying numerically the phase-ordering kinetics of a two-dimensional ferromagnetic Ising model with quenched disorder (either random bonds or random fields) we show that a critical percolation structure forms at an early stage. This structure is then rendered more and more compact by the ensuing coarsening process. Our results are compared to the nondisordered case, where a similar phenomenon is observed, and they are interpreted within a dynamical scaling framework.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, 132 Via Giovanni Paolo II, 84084 Fisciano, Salerno, Italy
- INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, 132 Via Giovanni Paolo II, 84084 Fisciano, Salerno, Italy
| | - Leticia F Cugliandolo
- Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Ferdinando Insalata
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, 132 Via Giovanni Paolo II, 84084 Fisciano, Salerno, Italy
- Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Marco Picco
- Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, Sorbonne Universités, 4 Place Jussieu, 75252 Paris Cedex 05, France
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18
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Corberi F, Zannetti M, Lippiello E, Burioni R, Vezzani A. Phase ordering in disordered and inhomogeneous systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062122. [PMID: 26172676 DOI: 10.1103/physreve.91.062122] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/26/2015] [Indexed: 06/04/2023]
Abstract
We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of dynamical behaviors characterized by different growth laws of the ordered domain size, namely logarithmic or power law, respectively. It is conjectured that the interplay between these dynamical classes is regulated by the same topological feature that governs the presence or the absence of a finite-temperature phase transition.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Fisica "E. R. Caianiello," and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
| | - Marco Zannetti
- Dipartimento di Fisica "E. R. Caianiello," and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
| | - Eugenio Lippiello
- Department of Mathematics and Physics, Second University of Naples, Viale Lincoln 5, 81100 Caserta, Italy
| | - Raffaella Burioni
- Dipartimento di Fisica e Scienza della Terra, and INFN, Gruppo Collegato di Parma, Università di Parma, Parco Area delle Scienze 7/A, I-423100 Parma, Italy
| | - Alessandro Vezzani
- Centro S3, CNR-Istituto di Nanoscienze, Via Campi 213A, 41125 Modena, Italy and Dipartimento di Fisica Scienza della Terra, Università di Parma, Parco Area delle Scienze 7/A, I-43100 Parma, Italy
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19
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Ahmad S, Puri S, Das SK. Phase separation of fluids in porous media: a molecular dynamics study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:040302. [PMID: 25375423 DOI: 10.1103/physreve.90.040302] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/21/2014] [Indexed: 06/04/2023]
Abstract
We present comprehensive molecular dynamics results for phase-separation kinetics of fluids in a porous medium. This system is modeled by a symmetric Lennard-Jones fluid mixture with a quenched random field. The presence of disorder slows down domain growth from power-law to a logarithmic form. It also modifies the correlation functions and structure factors which characterize the morphology. In particular, the structure-factor tail shows a non-Porod behavior, which is the consequence of scattering from rough interfaces.
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Affiliation(s)
- Shaista Ahmad
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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20
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Shrivastav GP, Banerjee V, Puri S. Non-Porod behavior in systems with rough morphologies. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2014; 37:98. [PMID: 25348663 DOI: 10.1140/epje/i2014-14098-9] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2014] [Revised: 09/24/2014] [Accepted: 10/10/2014] [Indexed: 05/28/2023]
Abstract
Many experiments yield multi-scale morphologies which are smooth on some length scales and fractal on others. Accurate statements about morphological properties, e.g., roughness exponent, fractal dimension, domain size, interfacial width, etc. are obtained from the correlation function and structure factor. In this paper, we present structure factor data for two systems: (a) droplet-in-droplet morphologies of double-phase-separating mixtures; and (b) ground-state morphologies in dilute anti-ferromagnets. An important characteristic of the scattering data is a non-Porod tail, which is associated with scattering off rough domains and interfaces.
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Affiliation(s)
- Gaurav P Shrivastav
- School of Physical Sciences, Jawaharlal Nehru University, 110067, New Delhi, 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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Patra S, Das SK. A comparative study of nonequilibrium dynamics in complex and real Ginzburg-Landau equations. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2013; 36:130. [PMID: 24248214 DOI: 10.1140/epje/i2013-13130-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2013] [Revised: 08/14/2013] [Accepted: 10/23/2013] [Indexed: 06/02/2023]
Abstract
Complex and real Ginzburg-Landau equations have been numerically studied by implementing Euler discretization technique. In addition to characterizing the differences and similarities of patterns involving these two continuum dynamical equations, in a wide range of appropriate parameter space, we have also made quantitative comparisons of growth dynamics in the two cases. In most part of the above-mentioned parameter space the complex Ginzburg-Landau equation exhibits frozen spiral dynamics. Results on the unlocking of this freezing are also presented.
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Affiliation(s)
- Saugata Patra
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O, 560064, Bangalore, India
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23
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Corberi F, Lippiello E, Mukherjee A, Puri S, Zannetti M. Scaling in the aging dynamics of the site-diluted Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042129. [PMID: 24229138 DOI: 10.1103/physreve.88.042129] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/20/2013] [Indexed: 06/02/2023]
Abstract
We study numerically the phase-ordering kinetics of the two-dimensional site-diluted Ising model. The data can be interpreted in a framework motivated by renormalization-group concepts. Apart from the usual fixed point of the nondiluted system, there exist two disorder fixed points, characterized by logarithmic and power-law growth of the ordered domains. This structure gives rise to a rich scaling behavior, with an interesting crossover due to the competition between fixed points, and violation of superuniversality.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Fisica "E. R. Caianiello", and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Ponte don Melillo, 84084 Fisciano (SA), Italy
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24
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Grynberg MD, Stinchcombe RB. Nonuniversal disordered Glauber dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:062102. [PMID: 23848622 DOI: 10.1103/physreve.87.062102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2013] [Indexed: 06/02/2023]
Abstract
We consider the one-dimensional Glauber dynamics with coupling disorder in terms of bilinear fermion Hamiltonians. Dynamic exponents embodied in the spectrum gap of these latter are evaluated numerically by averaging over both binary and Gaussian disorder realizations. In the first case, these exponents are found to follow the nonuniversal values of those of plain dimerized chains. In the second situation their values are still nonuniversal and subdiffusive below a critical variance above which, however, the relaxation time is suggested to grow as a stretched exponential of the equilibrium correlation length.
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Affiliation(s)
- Marcelo D Grynberg
- Departamento de Física, Universidad Nacional de La Plata, 1900 La Plata, Argentina
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25
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Das SK. Unlocking of frozen dynamics in the complex Ginzburg-Landau equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:012135. [PMID: 23410311 DOI: 10.1103/physreve.87.012135] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2012] [Revised: 12/20/2012] [Indexed: 06/01/2023]
Abstract
We present results for pattern formation and related dynamics in the two-dimensional complex Ginzburg-Landau equation. Both single and multispiral morphologies have been considered. For the former, Hagan's solution has been tested. In case of the multispiral morphology, at a late time, depending upon certain parameter values, the dynamics is found to be frozen. However, upon introduction of disorder in these parameters the frozen dynamics is observed to be unlocked. This latter result is counterintuitive considering our current knowledge of dynamics in disorder systems. We also present results for the role of shocks (the regions where Hagan's solution is violated) in the multispiral dynamics. It is observed that the suppression of the order-parameter amplitude, in this region, to the value allowed by Hagan's single-spiral solution, also unlocks the dynamical freezing. In this case, both the pattern and dynamics are observed to be very similar to the the dynamical XY model.
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Affiliation(s)
- Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India.
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26
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Corberi F, Lippiello E, Mukherjee A, Puri S, Zannetti M. Crossover in growth law and violation of superuniversality in the random-field Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:021141. [PMID: 22463186 DOI: 10.1103/physreve.85.021141] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2011] [Indexed: 05/31/2023]
Abstract
We study the nonconserved phase-ordering dynamics of the d=2,3 random-field Ising model, quenched to below the critical temperature. Motivated by the puzzling results of previous work in two and three dimensions, reporting a crossover from power-law to logarithmic growth, together with superuniversal behavior of the correlation function, we have undertaken a careful investigation of both the domain growth law and the autocorrelation function. Our main results are as follows: We confirm the crossover to asymptotic logarithmic behavior in the growth law, but, at variance with previous findings, we find the exponent in the preasymptotic power law to be disorder dependent, rather than being that of the pure system. Furthermore, we find that the autocorrelation function does not display superuniversal behavior. This restores consistency with previous results for the d=1 system, and fits nicely into the unifying scaling scheme we have recently proposed in the study of the random-bond Ising model.
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Affiliation(s)
- F Corberi
- Dipartimento di Fisica E. Caianiello and CNISM, Unità di Salerno, Università di Salerno, via Ponte don Melillo, 84084 Fisciano (SA), Italy
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27
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Vashishtha M, Jaiswal PK, Khanna R, Puri S, Sharma A. Spinodal phase separation in liquid films with quenched disorder. Phys Chem Chem Phys 2010; 12:12964-8. [PMID: 20838676 DOI: 10.1039/c0cp00776e] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We study spinodal phase separation in unstable thin liquid films on chemically disordered substrates via simulations of the thin-film equation. The disorder is characterized by immobile patches of varying size and Hamaker constant. The effect of disorder is pronounced in the early stages (amplification of fluctuations), remains during the intermediate stages and vanishes in the late stages (domain growth). These findings are in contrast to the well-known effects of quenched disorder in usual phase-separation processes, viz. the early stages remain undisturbed and domain growth is slowed down in the asymptotic regime. We also address the inverse problem of estimating disorder by thin-film experiments.
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Affiliation(s)
- Manish Vashishtha
- Department of Chemical Engineering, Indian Institute of Technology Delhi, New Delhi, India
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28
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Loureiro MPO, Arenzon JJ, Cugliandolo LF, Sicilia A. Curvature-driven coarsening in the two-dimensional Potts model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:021129. [PMID: 20365552 DOI: 10.1103/physreve.81.021129] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2009] [Indexed: 05/29/2023]
Abstract
We study the geometric properties of polymixtures after a sudden quench in temperature. We mimic these systems with the q -states Potts model on a square lattice with and without weak quenched disorder, and their evolution with Monte Carlo simulations with nonconserved order parameter. We analyze the distribution of hull-enclosed areas for different initial conditions and compare our results with recent exact and numerical findings for q=2 (Ising) case. Our results demonstrate the memory of the presence or absence of long-range correlations in the initial state during the coarsening regime and exhibit superuniversality properties.
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Affiliation(s)
- Marcos P O Loureiro
- Instituto de Física and INCT Sistemas Complexos, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre, RS, Brazil
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29
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Echeverria C, Tucci K, Cosenza MG. Phase growth in bistable systems with impurities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:016204. [PMID: 18351923 DOI: 10.1103/physreve.77.016204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2007] [Indexed: 05/26/2023]
Abstract
A system of coupled chaotic bistable maps on a lattice with randomly distributed impurities is investigated as a model for studying the phenomenon of phase growth in nonuniform media. The statistical properties of the system are characterized by means of the average size of spatial domains of equivalent spin variables that define the phases. It is found that the rate at which phase domains grow becomes smaller when impurities are present and that the average size of the resulting domains in the inhomogeneous state of the system decreases when the density of impurities is increased. The phase diagram showing regions where homogeneous, heterogeneous, and chessboard patterns occur on the space of parameters of the system is obtained. A critical boundary that separates the regime of slow growth of domains from the regime of fast growth in the heterogeneous region of the phase diagram is calculated. The transition between these two growth regimes is explained in terms of the stability properties of the local phase configurations. Our results show that the inclusion of spatial inhomogeneities can be used as a control mechanism for the size and growth velocity of phase domains forming in spatiotemporal systems.
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Affiliation(s)
- C Echeverria
- Laboratorio de Física Aplicada y Computacional, Universidad Nacional Experimental del Táchira, San Cristóbal, Venezuela
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30
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Paul R, Schehr G, Rieger H. Superaging in two-dimensional random ferromagnets. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:030104. [PMID: 17500658 DOI: 10.1103/physreve.75.030104] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/13/2006] [Indexed: 05/15/2023]
Abstract
We study the aging properties, in particular the two-time autocorrelations, of the two-dimensional randomly diluted Ising ferromagnet below the critical temperature via Monte Carlo simulations. We find that the autocorrelation function displays additive aging C(t,t{w})=C{st}(t)+C{ag}(t,t{w}), where the stationary part Cst} decays algebraically. The aging part shows anomalous scaling C{ag}(t,t{w})=C[h(t)h(t{w})], where h(u) is a nonhomogeneous function excluding a t/t{w} scaling.
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Affiliation(s)
- Raja Paul
- BIOMS, IWR, University of Heidelberg, D-69120 Heidelberg, Germany
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