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De Luca F, Ma X, Nardini C, Cates ME. Hyperuniformity in phase ordering: the roles of activity, noise, and non-constant mobility. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2024; 36:405101. [PMID: 38914094 DOI: 10.1088/1361-648x/ad5b45] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2024] [Accepted: 06/24/2024] [Indexed: 06/26/2024]
Abstract
Hyperuniformity emerges generically in the coarsening regime of phase-separating fluids. Numerical studies of active and passive systems have shown that the structure factorS(q) behaves asqςforq → 0, with hyperuniformity exponentς = 4. For passive systems, this result was explained in 1991 by a qualitative scaling analysis of Tomita, exploiting isotropy at scales much larger than the coarsening length. Here we reconsider and extend Tomita's argument to address cases of active phase separation and of non-constant mobility, again findingς = 4. We further show that dynamical noise of varianceDcreates a transientς = 2 regime forq^≪q^∗∼Dt[1-(d+2)ν]/2, crossing over toς = 4 at largerq^. Here,νis the coarsening exponent for the domain sizeℓ, such thatℓ(t)∼tν, andq^∝qℓis the rescaled wavenumber. In diffusive coarseningν=1/3, so the rescaled crossover wavevectorq^∗vanishes at large times whend⩾2. The slowness of this decay suggests a natural explanation for experiments that observe a long-livedς = 2 scaling in phase-separatingactivefluids (where noise is typically large). Conversely, ind = 1, we demonstrate that with noise theς = 2 regime survives ast→∞, withq^∗∼D5/6. (The structure factor is not then determined by the zero-temperature fixed point.) We confirm our analytical predictions by numerical simulations of continuum theories for active and passive phase separation in the deterministic case and of Model B for the stochastic case. We also compare them with related findings for a system near an absorbing-state transition rather than undergoing phase separation. A central role is played throughout by the presence or absence of a conservation law for the centre of mass positionRof the order parameter field.
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Affiliation(s)
- Filippo De Luca
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Xiao Ma
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Cesare Nardini
- Service de Physique de l'État Condensé, CEA, CNRS Université Paris-Saclay, CEA-Saclay, 91191 Gif-sur-Yvette, France
- Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, CNRS, Paris 75005, France
| | - Michael E Cates
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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Das SK, Das K, Vadakkayil N, Chakraborty S, Paul S. Initial correlation dependence of aging in phase separating solid binary mixtures and ordering ferromagnets. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:184005. [PMID: 31952063 DOI: 10.1088/1361-648x/ab6d10] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Following quenches of initial configurations having long range spatial correlations, prepared at the demixing critical point, to points inside the miscibility gap, we study aging phenomena in solid binary mixtures. Results on the decay of the two-time order-parameter autocorrelation functions, obtained from Monte Carlo simulations of the two-dimensional Ising model, with Kawasaki exchange kinetics, are analyzed via state-of-the art methods. The outcome is compared with that obtained for the ordering in uniaxial ferromagnets. For the latter, we have performed Monte Carlo simulations of the same model using the Glauber mechanism. For both types of systems we provide comparative discussion of our results with reference to those concerning quenches with configurations having no spatial correlation. We also discuss the role of structure on the decay of these correlations.
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Affiliation(s)
- Subir K Das
- Theoretical Sciences Unit and School of Advanced Materials, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur PO, Bangalore 560064, India
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Casiulis M, Tarzia M, Cugliandolo LF, Dauchot O. Ferromagnetism-induced phase separation in a two-dimensional spin fluid. J Chem Phys 2019; 150:154501. [PMID: 31005076 DOI: 10.1063/1.5064590] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the liquid-gas phase separation observed in a system of repulsive particles dressed with ferromagnetically aligning spins, a so-called "spin fluid." Microcanonical ensemble numerical simulations of finite-size systems reveal that magnetization sets in and induces a liquid-gas phase separation between a disordered gas and a ferromagnetic dense phase at low enough energies and large enough densities. The dynamics after a quench into the coexistence region show that the order parameter associated with the liquid-vapor phase separation follows an algebraic law with an unusual exponent, as it is forced to synchronize with the growth of the magnetization: this suggests that for finite size systems the magnetization sets in along a Curie line, which is also the gas-side spinodal line, and that the coexistence region ends at a tricritical point. This picture is confirmed at the mean-field level with different approximation schemes, namely, a Bethe lattice resolution and a virial expansion complemented by the introduction of a self-consistent Weiss-like molecular field. However, a detailed finite-size scaling analysis shows that in two dimensions the ferromagnetic phase escapes the Berezinskii-Kosterlitz-Thouless scenario and that the long-range order is not destroyed by the unbinding of topological defects. The Curie line thus becomes a magnetic crossover in the thermodynamic limit. Finally, the effects of the magnetic interaction range and those of the interaction softness are characterized within a mean-field semianalytical low-density approach.
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Affiliation(s)
- Mathias Casiulis
- Sorbonne Université, Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, 4 Place Jussieu, F-75005 Paris, France
| | - Marco Tarzia
- Sorbonne Université, Laboratoire de Physique Théorique de la Matière Condensée, CNRS UMR 7600, 4 Place Jussieu, F-75005 Paris, France
| | - Leticia F Cugliandolo
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Énergies, CNRS UMR 7589, 4 Place Jussieu, F-75005 Paris, France
| | - Olivier Dauchot
- PSL Research University, Laboratoire Gulliver, CNRS UMR 7083, ESPCI Paris, 10 rue Vauquelin, 75005 Paris, France
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Vadakkayil N, Chakraborty S, Das SK. Finite-size scaling study of aging during coarsening in non-conserved Ising model: The case of zero temperature quench. J Chem Phys 2019; 150:054702. [DOI: 10.1063/1.5052418] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Nalina Vadakkayil
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Saikat Chakraborty
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K. Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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Paul S, Das SK. Ballistic aggregation in systems of inelastic particles: Cluster growth, structure, and aging. Phys Rev E 2018; 96:012105. [PMID: 29347235 DOI: 10.1103/physreve.96.012105] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2016] [Indexed: 11/07/2022]
Abstract
We study far-from-equilibrium dynamics in models of freely cooling granular gas and ballistically aggregating compact clusters. For both the cases, from event-driven molecular dynamics simulations, we have presented detailed results on structure and dynamics in space dimensions d=1 and 2. Via appropriate analyses it has been confirmed that the ballistic aggregation mechanism applies in d=1 granular gases as well. Aging phenomena for this mechanism, in both the dimensions, have been studied via the two-time density autocorrelation function. This quantity is demonstrated to exhibit scaling property similar to that in the standard phase transition kinetics. The corresponding functional forms have been quantified and the outcomes have been discussed in connection with the structural properties. Our results on aging establish a more complete equivalence between the granular gas and the ballistic aggregation models in d=1.
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Affiliation(s)
- Subhajit Paul
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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Midya J, Majumder S, Das SK. Dimensionality dependence of aging in kinetics of diffusive phase separation: Behavior of order-parameter autocorrelation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:022124. [PMID: 26382361 DOI: 10.1103/physreve.92.022124] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2014] [Indexed: 06/05/2023]
Abstract
Behavior of two-time autocorrelation during the phase separation in solid binary mixtures is studied via numerical solutions of the Cahn-Hilliard equation as well as Monte Carlo simulations of the Ising model. Results are analyzed via state-of-the-art methods, including the finite-size scaling technique. Full forms of the autocorrelation in space dimensions 2 and 3 are obtained empirically. The long-time behavior is found to be power law, with exponents unexpectedly higher than the ones for the ferromagnetic ordering. Both Cahn-Hilliard and Ising models provide consistent results.
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Affiliation(s)
- Jiarul Midya
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Suman Majumder
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
| | - Subir K Das
- Theoretical Sciences Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur P.O., Bangalore 560064, India
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Dong RH, Zheng B, Zhou NJ. Critical domain-wall dynamics of model B. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:051125. [PMID: 19518434 DOI: 10.1103/physreve.79.051125] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2009] [Indexed: 05/27/2023]
Abstract
With Monte Carlo methods, we simulate the critical domain-wall dynamics of model B, taking the two-dimensional Ising model as an example. In the macroscopic short-time regime, a dynamic scaling form is revealed. Due to the existence of the quasirandom walkers, the magnetization shows intrinsic dependence on the lattice size L . An exponent which governs the L dependence of the magnetization is measured to be sigma=0.243(8) .
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Affiliation(s)
- R H Dong
- Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou 310027, People's Republic of China
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Sire C. Autocorrelation exponent of conserved spin systems in the scaling regime following a critical quench. PHYSICAL REVIEW LETTERS 2004; 93:130602. [PMID: 15524696 DOI: 10.1103/physrevlett.93.130602] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2004] [Indexed: 05/24/2023]
Abstract
We study the autocorrelation function of a conserved spin system following a quench at the critical temperature. Defining the correlation length L(t) approximately t(1/z), we find that for times t' and t satisfying L(t')<<L(t)<<L(t')(phi) well inside the scaling regime, the spin autocorrelation function behaves like s(t)s(t') approximately L(t')(-(d-2+eta))[L(t')/L(t)](lambda(')(c)). For the O(n) model in the n-->infinity limit, we show that lambda(')(c)=d+2 and phi=z/2. We give a heuristic argument suggesting that this result is, in fact, valid for any dimension d and spin vector dimension n. We present numerical simulations for the conserved Ising model in d=1 and d=2, which are fully consistent with the present theory.
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Affiliation(s)
- Clément Sire
- Laboratoire de Physique Théorique (UMR 5152 du CNRS), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex 4, France.
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Nagaya T, Gilli JM. Experimental study of spinodal decomposition in a 1D conserved order parameter system. PHYSICAL REVIEW LETTERS 2004; 92:145504. [PMID: 15089551 DOI: 10.1103/physrevlett.92.145504] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2002] [Indexed: 05/24/2023]
Abstract
We study the zigzag instability coarsening of splay-bend walls formed in a nematic liquid crystal under external fields. The vertexes of zigzag can be considered as kinks in a one-dimensional order parameter system and the geometrical constraints associated with the necessary equal length sum of zig and zag segments impose a conserved quantity in this Cahn-Hilliard-type problem. In the late stage of coarsening, the characteristic length of the system L(t) shows a logarithmic increase in time and the dynamical scaling law holds. We then try to extract the nontrivial asymptotic scaling exponent lambda of the two-time correlation function, defined by lim(<phi(0,t)phi(0,t('))> approximately [L(t)/L(t('))](-lambda). The scaling exponents with respective time references, t(')=32 and 64 s, after quench are found to be lambda approximately 2 which is larger than the value with respective time reference t(')=0, predicted by numerical simulation.
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Affiliation(s)
- Tomoyuki Nagaya
- Department of Electrical and Electronic Engineering, Faculty of Engineering, Okayama University, 3-1-1 Tsushimanaka Okayama, 700-8530 Japan
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Kim E, Kim B, Lee SJ. Nonequilibrium critical dynamics of the triangular antiferromagnetic Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:066127. [PMID: 14754289 DOI: 10.1103/physreve.68.066127] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/28/2003] [Revised: 08/29/2003] [Indexed: 05/24/2023]
Abstract
We investigate the nonequilibrium critical dynamics of antiferromagnetic Ising model on a two-dimensional triangular lattice via dynamic Monte Carlo simulation employing spin-flip kinetics. Macroscopic degeneracy of the ground state originating from geometric frustration fundamentally affects the nonequilibrium dynamics of the system. In particular, the defects and the loose spins (whose flip costs no energy) play key roles in the dynamics. The long-time evolution is characterized by a critical dynamic scaling with a growing length scale xi(t). With random initial configurations, xi(t) exhibits a subdiffusive growth in time, xi(t) approximately t(1/z) with 1/z approximately 0.43, while xi(t) shows a diffusive growth with z=2 for the relaxation within the dominant sector of the ground-state manifold. The nonequilibrium critical dynamics therefore exhibits an interesting initial-state dependence. Persistence and the two-time temporal properties are also discussed.
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Affiliation(s)
- Eunhye Kim
- Department of Physics, Changwon National University, Changwon 641-773, Korea
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Sch tz GM. Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/36/201] [Citation(s) in RCA: 108] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Corberi F, Castellano C, Lippiello E, Zannetti M. Universality of the off-equilibrium response function in the kinetic Ising chain. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 65:066114. [PMID: 12188790 DOI: 10.1103/physreve.65.066114] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2002] [Indexed: 05/23/2023]
Abstract
The off-equilibrium response function chi(t,t(w)) and autocorrelation function C(t,t(w)) of an Ising chain with spin-exchange dynamics are studied numerically and compared with the same quantities in the case of spin-flip dynamics. It is found that, even though these quantities are different in the two cases, the parametric plot of chi(t,t(w)) versus C(t,t(w)) is the same. While this result could be expected in higher dimensionality, where chi(C) is related to the equilibrium state, it is far from trivial in the one-dimensional case where this relation does not hold. The origin of the universality of chi(C) is traced back to the optimization of domains position with respect to the perturbing external field. This mechanism is investigated resorting to models with a single domain moving in a random environment.
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Affiliation(s)
- Federico Corberi
- Istituto Nazionale per la Fisica della Materia, Unità di Salerno and Dipartimento di Fisica, Università di Salerno, 84081 Baronissi (Salerno), Italy.
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Das J, Rao M. Ordering dynamics of heisenberg spins with torque: crossover, spin waves, and defects. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:1601-1612. [PMID: 11088621 DOI: 10.1103/physreve.62.1601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/24/2000] [Indexed: 05/23/2023]
Abstract
We study the effect of a torque induced by the local molecular field on the phase ordering dynamics of the Heisenberg model when the total magnetization is conserved. The torque drives the zero-temperature ordering dynamics to a new fixed point, characterized by exponents z=2 and lambda approximately 5. This "torque-driven" fixed point is approached at times such that t>>g(2), where g is the strength of the torque. All physical quantities, like the domain size L(t) and the equal and unequal time correlation functions, obey a crossover scaling form over the entire range of g. An attempt to understand this crossover behavior from the approximate Gaussian closure scheme fails completely, implying that the dynamics at late times cannot be understood from the dynamics of defects alone. We provide convincing arguments that the spin configurations can be decomposed in terms of defects and spin waves which interact with each other even at late times. In the absence of the torque term, the spin waves decay faster, but even so we find that the Gaussian closure scheme is inconsistent. In the latter case the inconsistency may be remedied by including corrections to a simple Gaussian distribution. For completeness we include a discussion of the ordering dynamics at T(c), where the torque is shown to be relevant, with exponents z=4-varepsilon/2 and lambda=d (where varepsilon=6-d). We show to all orders in perturbation theory that lambda=d as a consequence of the conservation law.
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Affiliation(s)
- J Das
- Institute of Mathematical Sciences, Taramani, Chennai 600113, India and Raman Research Institute, C.V. Raman Avenue, Sadashivanagar, Bangalore 560080, India
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Shrestha SP, Pandey D. Kinetics of martensitic type restacking transitions: dynamic scaling, universal growth exponent and evolution of diffuse scattering. Proc Math Phys Eng Sci 1997. [DOI: 10.1098/rspa.1997.0072] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- Shankar Prasad Shrestha
- School of Materials Science and Technology, Banaras Hindu University, Varanasi 221005, India
| | - Dhananjai Pandey
- School of Materials Science and Technology, Banaras Hindu University, Varanasi 221005, India
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Yeung C, Rao M, Desai RC. Bounds on the decay of the autocorrelation in phase ordering dynamics. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:3073-3077. [PMID: 9964613 DOI: 10.1103/physreve.53.3073] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Majumdar SN, Sengupta AM. Nonequilibrium dynamics following a quench to the critical point in a semi-infinite system. PHYSICAL REVIEW LETTERS 1996; 76:2394-2397. [PMID: 10060686 DOI: 10.1103/physrevlett.76.2394] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Marko JF, Barkema GT. Phase ordering in the Ising model with conserved spin. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:2522-2534. [PMID: 9963695 DOI: 10.1103/physreve.52.2522] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Sire C, Majumdar SN. Coarsening in the q-state Potts model and the Ising model with globally conserved magnetization. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:244-254. [PMID: 9963428 DOI: 10.1103/physreve.52.244] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Majumdar SN, Huse DA. Growth of long-range correlations after a quench in phase-ordering systems. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1995; 52:270-284. [PMID: 9963430 DOI: 10.1103/physreve.52.270] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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