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Gessert D, Christiansen H, Janke W. Aging following a zero-temperature quench in the d=3 Ising model. Phys Rev E 2024; 109:044148. [PMID: 38755941 DOI: 10.1103/physreve.109.044148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2023] [Accepted: 03/25/2024] [Indexed: 05/18/2024]
Abstract
Aging in phase-ordering kinetics of the d=3 Ising model following a quench from infinite to zero temperature is studied by means of Monte Carlo simulations. In this model the two-time spin-spin autocorrelator C_{ag} is expected to obey dynamical scaling and to follow asymptotically a power-law decay with the autocorrelation exponent λ. Previous work indicated that the lower Fisher-Huse bound of λ≥d/2=1.5 is violated in this model. Using much larger systems than previously studied, the instantaneous exponent for λ we obtain at late times does not disagree with this bound. By conducting systematic fits to the data of C_{ag} using different Ansätze for the leading correction term, we find λ=1.58(14), with most of the error attributed to the systematic uncertainty regarding the Ansätze. This result is in contrast to the recent report that below the roughening transition universality might be violated.
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Affiliation(s)
- Denis Gessert
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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Corberi F, Lippiello E, Politi P. Quasideterministic dynamics, memory effects, and lack of self-averaging in the relaxation of quenched ferromagnets. Phys Rev E 2020; 102:020102. [PMID: 32942398 DOI: 10.1103/physreve.102.020102] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2020] [Accepted: 08/06/2020] [Indexed: 11/07/2022]
Abstract
We discuss the interplay between the degree of dynamical stochasticity, memory persistence, and violation of the self-averaging property in the aging kinetics of quenched ferromagnets. We show that, in general, the longest possible memory effects, which correspond to the slowest possible temporal decay of the correlation function, are accompanied by the largest possible violation of self-averaging and a quasideterministic descent into the ergodic components. This phenomenon is observed in different systems, such as the Ising model with long-range interactions, including the mean-field, and the short-range random-field Ising model.
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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
| | - Eugenio Lippiello
- Dipartimento di Matematica e Fisica, Università della Campania, Viale Lincoln 5, 81100 Caserta, Italy
| | - Paolo Politi
- Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, Via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy.,INFN Sezione di Firenze, via G. Sansone 1, 50019 Sesto Fiorentino, Italy
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Corberi F, Kumar M, Lippiello E, Puri S. Effects of frustration on fluctuation-dissipation relations. Phys Rev E 2019; 99:012131. [PMID: 30780308 DOI: 10.1103/physreve.99.012131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2018] [Indexed: 06/09/2023]
Abstract
We study numerically the aging properties of the two-dimensional Ising model with quenched disorder considered in our recent paper [Phys. Rev. E 95, 062136 (2017)2470-004510.1103/PhysRevE.95.062136], where frustration can be tuned by varying the fraction of antiferromagnetic interactions. Specifically, we focus on the scaling properties of the autocorrelation and linear response functions after a quench of the model to a low temperature. We find that the interplay between equilibrium and aging occurs differently in the various regions of the phase diagram of the model. When the quench is made into the ferromagnetic phase the two-time quantities are made by the sum of an equilibrium and an aging part, whereas in the paramagnetic phase these parts combine in a multiplicative way. Scaling forms are shown to be obeyed with good accuracy, and the corresponding exponents and scaling functions are determined and discussed in the framework of what is known in clean and disordered systems.
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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
- International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India
| | - Eugenio Lippiello
- Department of Mathematics and Physics, University of Campania "L. Vanvitelli", Viale Lincoln 5, 81100 Caserta, Italy
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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Minic D, Pleimling M. Correspondence between nonrelativistic anti-de Sitter space and conformal field theory, and aging-gravity duality. Phys Rev E 2009; 78:061108. [PMID: 19256803 DOI: 10.1103/physreve.78.061108] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2008] [Indexed: 11/07/2022]
Abstract
We point out that the recent discussion of nonrelativistic anti-de Sitter space and conformal field theory correspondence has a direct application in nonequilibrium statistical physics, a fact which has not been emphasized in the recent literature on the subject. In particular, we propose a duality between aging in systems far from equilibrium characterized by the dynamical exponent z=2 and gravity in a specific background. The key ingredient in our proposal is the recent geometric realization of the Schrödinger group. We also discuss the relevance of the proposed correspondence for the more general aging phenomena in systems where the value of the dynamical exponent is different from 2.
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Affiliation(s)
- Djordje Minic
- Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435, USA.
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Ferrera A, Luque B, Lacasa L, Valero E. Self-overlap as a method of analysis in Ising models. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:061103. [PMID: 17677216 DOI: 10.1103/physreve.75.061103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2006] [Revised: 03/05/2007] [Indexed: 05/16/2023]
Abstract
The damage spreading (DS) method provided a useful tool to obtain analytical results of the thermodynamics and stability of the two-dimensional (2D) Ising model--amongst many others--but it suffered both from ambiguities in its results and from large computational costs. In this paper we propose an alternative method, the so-called self-overlap method, based on the study of correlation functions measured at subsequent time steps as the system evolves towards its equilibrium. Applying Markovian and mean-field approximations to a 2D Ising system we obtain both analytical and numerical results on the thermodynamics that agree with the expected behavior. We also provide some analytical results on the stability of the system. Since only a single replica of the system needs to be studied, this method would seem to be free from the ambiguities that afflicted the DS method. It also seems to be numerically more efficient and analytically simpler.
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Affiliation(s)
- A Ferrera
- Departamento de Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, E-28040 Madrid, Spain
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Röthlein A, Baumann F, Pleimling M. Symmetry-based determination of space-time functions in nonequilibrium growth processes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:061604. [PMID: 17280075 DOI: 10.1103/physreve.74.061604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2006] [Indexed: 05/13/2023]
Abstract
We study the space-time correlation and response functions in nonequilibrium growth processes described by linear stochastic Langevin equations. Exploiting exclusively the existence of space- and time-dependent symmetries of the noiseless part of these equations, we derive expressions for the universal scaling functions of two-time quantities which are found to agree with the exact expressions obtained from the stochastic equations of motion. The usefulness of the space-time functions is illustrated through the investigation of two atomistic growth models, the Family model and the restricted Family model, which are shown to belong to a unique universality class in 1+1 and 2+1 space dimensions. This corrects earlier studies which claimed that in 2+1 dimensions the two models belong to different universality classes.
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Affiliation(s)
- Andreas Röthlein
- Institut für Theoretische Physik I, Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
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Enss T, Henkel M, Picone A, Schollwöck U. Ageing phenomena without detailed balance: the contact process. ACTA ACUST UNITED AC 2004. [DOI: 10.1088/0305-4470/37/44/002] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Ramasco JJ, Henkel M, Santos MA, Santos CADS. Ageing in the critical contact process: a Monte Carlo study. ACTA ACUST UNITED AC 2004. [DOI: 10.1088/0305-4470/37/44/003] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Henkel M, Paessens M, Pleimling M. Scaling of the linear response in simple aging systems without disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:056109. [PMID: 15244885 DOI: 10.1103/physreve.69.056109] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2003] [Indexed: 05/24/2023]
Abstract
The time-dependent scaling of the thermoremanent and zero-field-cooled susceptibilities in ferromagnetic spin systems undergoing aging after a quench to a temperature at or below criticality is studied. A recent debate on their interpretation is resolved by showing that for systems with a short-ranged equilibrium spin-spin correlator and above their roughening temperature, the field-cooled susceptibility chi(FC)(t)-chi(0) approximately t(-A), where chi(0) is related to the equilibrium magnetization and the exponent A is related to the time-dependent scaling of the interface width between ordered domains. The same effect also dominates the scaling of the zero-field-cooled susceptibility chi(ZFC)(t,s), but does not enter into the thermoremanent susceptibility rho(TRM)(t,s). However, there may be large finite-time corrections to the scaling of rho(TRM)(t,s) which are explicitly derived and may be needed in order to extract reliable aging exponents. Consistency with the predictions of local scale invariance is confirmed in the Glauber-Ising and spherical models.
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Affiliation(s)
- Malte Henkel
- Laboratoire de Physique des Matériaux, Laboratoie Associé au CNRS, UMR 7556, Université Henri Poincaré Nancy I, Boîte Postale 239, F-54506 Vandoeuvre lès Nancy Cedex, France
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Abstract
Mycotoxins are natural contaminants whose presence in food- and feedstuffs cannot be completely avoided. Since several mycotoxins have been associated with and implicated in human and animal diseases there is a need to establish maximum levels, guidelines or action levels for them in some kinds of commodities. International and government authorities in many countries have been investing in mycotoxins research and initiating administrative actions for elaboration of legislation and implementing regulatory measures for the control of mycotoxins. Codex Alimentarius Commission is established international legislation on food and feed. In European Union specific limits and regulations for mycotoxins and other contaminants are constructed under the general Codex standards and based on proposal from European Commission. The legal basis for European Commission became available with the framework Council Regulation (EEC) No 315/93. In this paper, legislation regarding maximum levels for certain mycotoxins in food- and feedstuffs in European Community and other countries were reviewed and discussed.
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Affiliation(s)
- J Zmudzki
- Department of Pharmacology and Toxicology, National Veterinary Institute in Puławy, Al Partyzantów 57, 24-100 Puławy, Poland.
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