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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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Corberi F, Villavicencio-Sanchez R. Role of initial state and final quench temperature on aging properties in phase-ordering kinetics. Phys Rev E 2016; 93:052105. [PMID: 27300828 DOI: 10.1103/physreve.93.052105] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2016] [Indexed: 11/07/2022]
Abstract
We study numerically the two-dimensional Ising model with nonconserved dynamics quenched from an initial equilibrium state at the temperature T_{i}≥T_{c} to a final temperature T_{f} below the critical one. By considering processes initiating both from a disordered state at infinite temperature T_{i}=∞ and from the critical configurations at T_{i}=T_{c} and spanning the range of final temperatures T_{f}∈[0,T_{c}[ we elucidate the role played by T_{i} and T_{f} on the aging properties and, in particular, on the behavior of the autocorrelation C and of the integrated response function χ. Our results show that for any choice of T_{f}, while the autocorrelation function exponent λ_{C} takes a markedly different value for T_{i}=∞ [λ_{C}(T_{i}=∞)≃5/4] or T_{i}=T_{c} [λ_{C}(T_{i}=T_{c})≃1/8] the response function exponents are unchanged. Supported by the outcome of the analytical solution of the solvable spherical model we interpret this fact as due to the different contributions provided to autocorrelation and response by the large-scale properties of the system. As changing T_{f} is considered, although this is expected to play no role in the large-scale and long-time properties of the system, we show important effects on the quantitative behavior of χ. In particular, data for quenches to T_{f}=0 are consistent with a value of the response function exponent λ_{χ}=1/2λ_{C}(T_{i}=∞)=5/8 different from the one [λ_{χ}∈(0.5-0.56)] found in a wealth of previous numerical determinations in quenches to finite final temperatures. This is interpreted as due to important preasymptotic corrections associated to T_{f}>0.
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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
| | - Rodrigo Villavicencio-Sanchez
- Dipartimento di Fisica "E. R. Caianiello", Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
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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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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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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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Corberi F, Lippiello E, Sarracino A, Zannetti M. Fluctuation-dissipation relations and field-free algorithms for the computation of response functions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:011124. [PMID: 20365340 DOI: 10.1103/physreve.81.011124] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2009] [Indexed: 05/29/2023]
Abstract
We discuss the relation between the fluctuation-dissipation relation derived by Chatelain and Ricci-Tersenghi [C. Chatelain, J. Phys. A 36, 10739 (2003); F. Ricci-Tersenghi, Phys. Rev. E 68, 065104(R) (2003)] and that by Lippiello-Corberi-Zannetti [E. Lippiello, F. Corberi, and M. Zannetti, Phys. Rev. E 71, 036104 (2005)]. In order to do that, we rederive the fluctuation-dissipation relation for systems of discrete variables evolving in discrete time via a stochastic nonequilibrium Markov process. The calculation is carried out in a general formalism comprising the Chatelain, Ricci-Tersenghi, result and that by Lippiello-Corberi-Zannetti as special cases. The applicability, generality, and experimental feasibility of the two approaches are thoroughly discussed. Extending the analytical calculation to the variance of the response function, we show the advantage of field-free numerical methods with respect to the standard method, where the perturbation is applied. We also show that the signal-to-noise ratio is better (by a factor square root of 2) in the algorithm of Lippiello-Corberi-Zannetti with respect to that of Chatelain-Ricci Tersenghi.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Matematica ed Informatica and INFN, Gruppo Collegato di Salerno and CNISM, Unitá di Salerno, Università di Salerno, Via Ponte don Melillo, Fisciano (SA), Italy
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Lippiello E, Corberi F, Sarracino A, Zannetti M. Nonlinear response and fluctuation-dissipation relations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:041120. [PMID: 18999392 DOI: 10.1103/physreve.78.041120] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2008] [Indexed: 05/27/2023]
Abstract
A unified derivation of the off-equilibrium fluctuation dissipation relations (FDRs) is given for Ising and continuous spins to arbitrary order, within the framework of Markovian stochastic dynamics. Knowledge of the FDRs allows one to develop zero field algorithms for the efficient numerical computation of the response functions. Two applications are presented. In the first one, the problem of probing for the existence of a growing cooperative length scale is considered in those cases, like in glassy systems, where the linear FDR is of no use. The effectiveness of an appropriate second order FDR is illustrated in the test case of the Edwards-Anderson spin glass in one and two dimensions. In the second application, the important problem of the definition of an off-equilibrium effective temperature through the nonlinear FDR is considered. It is shown that, in the case of coarsening systems, the effective temperature derived from the second order FDR is consistent with the one obtained from the linear FDR.
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Affiliation(s)
- Eugenio Lippiello
- Dipartimento di Scienze Fisiche, Universitá di Napoli Federico II, Naples, Italy.
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Corberi F, Lippiello E, Zannetti M. Influence of thermal fluctuations on the geometry of interfaces of the quenched Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:011109. [PMID: 18763921 DOI: 10.1103/physreve.78.011109] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2008] [Indexed: 05/26/2023]
Abstract
We study the role of the quench temperature Tf in the phase-ordering kinetics of the Ising model with single spin flip in d=2,3 . Equilibrium interfaces are flat at Tf=0 , whereas at Tf>0 they are curved and rough (above the roughening temperature in d=3 ). We show, by means of scaling arguments and numerical simulations, that this geometrical difference is important for the phase-ordering kinetics as well. In particular, while the growth exponent z=2 of the size of domains L(t) approximately t 1/z is unaffected by Tf, other exponents related to the interface geometry take different values at Tf=0 or Tf>0 . For Tf>0 a crossover phenomenon is observed from an early stage where interfaces are still flat and the system behaves as at Tf=0 , to the asymptotic regime with curved interfaces characteristic of Tf>0 . Furthermore, it is shown that the roughening length, although subdominant with respect to L(t) , produces appreciable correction to scaling up to very long times in d=2 .
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Affiliation(s)
- Federico Corberi
- Dipartimento di Matematica ed Informatica, Università di Salerno, via Ponte don Melillo, Fisciano SA, Italy
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Burioni R, Cassi D, Corberi F, Vezzani A. Phase-ordering kinetics on graphs. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:011113. [PMID: 17358116 DOI: 10.1103/physreve.75.011113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2006] [Indexed: 05/14/2023]
Abstract
We study numerically the phase-ordering kinetics following a temperature quench of the Ising model with single spin-flip dynamics on a class of graphs, including geometrical fractals and random fractals, such as the percolation cluster. For each structure we discuss the scaling properties and compute the dynamical exponents. We show that the exponent a_{chi} for the integrated response function, at variance with all the other exponents, is independent of temperature and of the presence of pinning. This universal character suggests a strict relation between a_{chi} and the topological properties of the networks, in analogy to what is observed on regular lattices.
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Affiliation(s)
- R Burioni
- Dipartimento di Fisica and INFN, Università di Parma, Parco Area delle Scienze 7/A, I-423100 Parma, Italy
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Corberi F, Lippiello E, Zannetti M. Scaling and universality in the aging kinetics of the two-dimensional clock model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:041106. [PMID: 17155021 DOI: 10.1103/physreve.74.041106] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/02/2005] [Revised: 07/04/2006] [Indexed: 05/12/2023]
Abstract
We study numerically the aging dynamics of the two-dimensional p -state clock model after a quench from an infinite temperature to the ferromagnetic phase or to the Kosterlitz-Thouless phase. The system exhibits the general scaling behavior characteristic of nondisordered coarsening systems. For quenches to the ferromagnetic phase, the value of the dynamical exponents suggests that the model belongs to the Ising-type universality class. Specifically, for the integrated response function chi(t,s) approximately or = s(-a)chif(t/s), we find a(chi) consistent with the value a(chi)=0.28 found in the two-dimensional Ising model.
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Affiliation(s)
- Federico Corberi
- Istituto Nazionale di Fisica della Materia, Unità di Salerno and Dipartimento di Fisica E.Caianiello, Università di Salerno, 84081 Baronissi (Salerno), Italy.
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Lippiello E, Corberi F, Zannetti M. Test of local scale invariance from the direct measurement of the response function in the Ising model quenched to and below T(C). PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:041113. [PMID: 17155028 DOI: 10.1103/physreve.74.041113] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2006] [Revised: 06/14/2006] [Indexed: 05/12/2023]
Abstract
In order to check on a recent suggestion that local scale invariance [M. Henkel, Phys. Rev. Lett. 87, 265701 (2001)] might hold when the dynamics is of Gaussian nature, we have carried out the measurement of the response function in the kinetic Ising model with Glauber dynamics quenched to T(C) in d=4, where Gaussian behavior is expected to apply, and in the two other cases of the d=2 model quenched to T(C) and to below T(C), where instead deviations from Gaussian behavior are expected to appear. We find that in the d=4 case there is an excellent agreement between the numerical data, the local scale invariance prediction and the analytical Gaussian approximation. No logarithmic corrections are numerically detected. Conversely, in the d=2 cases, both in the quench to T(C) and to below T(C), sizable deviations of the local scale invariance behavior from the numerical data are observed. These results do support the idea that local scale invariance might miss to capture the non-Gaussian features of the dynamics. The considerable precision needed for the comparison has been achieved through the use of a fast new algorithm for the measurement of the response function without applying the external field. From these high quality data we obtain a=0.27+/-0.002 for the scaling exponent of the response function in the d=2 Ising model quenched to below T(C), in agreement with previous results.
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Affiliation(s)
- Eugenio Lippiello
- Istituto Nazionale di Fisica della Materia, Unità di Salerno and Dipartimento di Fisica E. Caianiello, Università di Salerno, 84081 Baronissi (Salerno), Italy.
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Burioni R, Cassi D, Corberi F, Vezzani A. Aging dynamics and the topology of inhomogenous networks. PHYSICAL REVIEW LETTERS 2006; 96:235701. [PMID: 16803384 DOI: 10.1103/physrevlett.96.235701] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2005] [Indexed: 05/10/2023]
Abstract
We study phase ordering on networks and we establish a relation between the exponent a(x) of the aging part of the integrated auto-response function and the topology of the underlying structures. We show that a(x) > 0 in full generality on networks which are above the lower critical dimension d(L), i.e., where the corresponding statistical model has a phase transition at finite temperature. For discrete symmetry models on finite ramified structures with T(c) = 0, which are at the lower critical dimension d(L), we show that a(x) is expected to vanish. We provide numerical results for the physically interesting case of the 2 - d percolation cluster at or above the percolation threshold, i.e., at or above d(L), and for other networks, showing that the value of a(x) changes according to our hypothesis. For O(N) models we find that the same picture holds in the large-N limit and that a(x) only depends on the spectral dimension of the network.
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Affiliation(s)
- R Burioni
- Dipartimento di Fisica and INFN, Università di Parma, Parco Area delle Scienze 7/A, I-423100 Parma, Italy
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Andrenacci N, Corberi F, Lippiello E. Fluctuation-dissipation relation in an Ising model without detailed balance. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:046124. [PMID: 16711895 DOI: 10.1103/physreve.73.046124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2005] [Indexed: 05/09/2023]
Abstract
We consider the modified Ising model introduced by de Oliveira, Mendes, and Santos [J. Phys. A 26, 2317 (1993)], where the temperature depends locally on the spin configuration and detailed balance and local equilibrium are not obeyed. We derive a relation between the linear response function and correlation functions that generalizes the fluctuation-dissipation theorem. In the stationary states of the model, which are the counterparts of the Ising equilibrium states, the fluctuation-dissipation theorem breaks down due to the lack of time reversal invariance. In the nonstationary phase-ordering kinetics, the parametric plot of the integrated response function chi(t,t(w)) vs the autocorrelation function is different from that of the kinetic Ising model. However, splitting chi(t,t(w)) into a stationary and an aging term chi(t,t(w)) = chi(st)(t-t(w)) + chi(ag)(t,t(w)), we find chi(ag)(t,t(w)) approximately t(w)(-a(chi)) f(t/t(w)), and a numerical value of a(chi) consistent with a(chi)= 1/4, as in the kinetic Ising model.
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Affiliation(s)
- Natascia Andrenacci
- Istituto Nazionale di Fisica della Materia, Unità di Salerno and Dipartimento di Fisica E.R.Caianiello, Università di Salerno, 84081 Baronissi (Salerno), Italy.
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Corberi F, Lippiello E, Zannetti M. Correction to scaling in the response function of the two-dimensional kinetic Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:056103. [PMID: 16383684 DOI: 10.1103/physreve.72.056103] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2004] [Revised: 07/27/2005] [Indexed: 05/05/2023]
Abstract
The aging part Rag(t,s) of the impulsive response function of the two-dimensional ferromagnetic Ising model, quenched below the critical point, is studied numerically employing an algorithm without the imposition of the external field. We find that the simple scaling form Rag(t,s)=s-(1+a)f(t/s), which is usually believed to hold in the aging regime, is not obeyed. We analyze the data assuming the existence of a correction to scaling. We find a=0.273+/-0.006, in agreement with previous numerical results obtained from the zero field cooled magnetization. We investigate in detail also the scaling function f(t/s) and we compare the results with the predictions of analytical theories. We make an ansatz for the correction to scaling, deriving an analytical expression for Rag(t,s). This gives a satisfactory qualitative agreement with the numerical data for Rag(t,s) and for the integrated response functions. With the analytical model we explore the overall behavior, extrapolating beyond the time regime accessible with the simulations. We explain why the data for the zero field cooled susceptibility are not too sensitive to the existence of the correction to scaling in Rag(t,s), making this quantity the most convenient for the study of the asymptotic scaling properties.
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Affiliation(s)
- Federico Corberi
- Istituto Nazionale di Fisica della Materia, Unità di Salerno and Dipartimento di Fisica "E. Caianiello," Università di Salerno, 84081 Baronissi (Salerno), Italy.
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Corberi F, Lippiello E, Zannetti M. Comment on "Scaling of the linear response in simple aging systems without disorder". PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:028103; discussion 028104. [PMID: 16196763 DOI: 10.1103/physreve.72.028103] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/25/2004] [Indexed: 05/04/2023]
Abstract
We have repeated the simulations of Henkel, Paessens, and Pleimling (HPP) [Phys. Rev. E 69, 056109 (2004)] for the field-cooled susceptibility chi(FC)(t) - chi0 approximately t(-A) in the quench of ferromagnetic systems to and below T(C). We show that, contrary to the statement made by HPP, the exponent A coincides with the exponent a of the linear response function R(t,s) approximately s(-(1+a))f(R)(t/s). We point out what are the assumptions in the argument of HPP that lead them to the conclusion A < a.
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Affiliation(s)
- Federico Corberi
- Istituto Nazionale di Fisica della Materia, Unità di Salerno and Dipartimento di Fisica E.R. Caianiello, Università di Salerno, 84081 Baronissi (Salerno), Italy.
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Mayer P, Sollich P. Observable dependent quasi-equilibrium in slow dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:046113. [PMID: 15903732 DOI: 10.1103/physreve.71.046113] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/11/2004] [Revised: 02/15/2005] [Indexed: 05/02/2023]
Abstract
We present examples demonstrating that quasi-equilibrium fluctuation-dissipation behavior at short time differences is not a generic feature of systems with slow nonequilibrium dynamics. We analyze in detail the nonequilibrium fluctuation-dissipation ratio X(t, t(w)) associated with a defect-pair observable in the Glauber-Ising spin chain. It turns out that X not = 1 throughout the short-time regime and in particular X(t(w), t(w)) = 3/4 for t(w) --> infinity. The analysis is extended to observables detecting defects at a finite distance from each other, where similar violations of quasi-equilibrium behavior are found. We discuss our results in the context of metastable states, which suggests that a violation of short-time quasi-equilibrium behavior could occur in general glassy systems for appropriately chosen observables.
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Affiliation(s)
- Peter Mayer
- Department of Mathematics, King's College, Strand, London, WC2R 2LS, United Kingdom
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Lippiello E, Corberi F, Zannetti M. Off-equilibrium generalization of the fluctuation dissipation theorem for Ising spins and measurement of the linear response function. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:036104. [PMID: 15903490 DOI: 10.1103/physreve.71.036104] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/20/2004] [Revised: 10/21/2004] [Indexed: 05/02/2023]
Abstract
We derive for Ising spins an off-equilibrium generalization of the fluctuation dissipation theorem, which is formally identical to the one previously obtained for soft spins with Langevin dynamics [L.F. Cugliandolo, J. Kurchan, and G. Parisi, J. Phys. I 4, 1641 (1994)]. The result is quite general and holds both for dynamics with conserved and nonconserved order parameters. On the basis of this fluctuation dissipation relation, we construct an efficient numerical algorithm for the computation of the linear response function without imposing the perturbing field, which is alternative to those of Chatelain [J. Phys. A 36, 10 739 (2003)] and Ricci-Tersenghi [Phys. Rev. E 68, 065104(R) (2003)]. As applications of the new algorithm, we present very accurate data for the linear response function of the Ising chain, with conserved and nonconserved order parameter dynamics, finding that in both cases the structure is the same with a very simple physical interpretation. We also compute the integrated response function of the two-dimensional Ising model, confirming that it obeys scaling chi (t, t(w)) approximately equal to t(-a)(w) f (t/t(w)) , with a =0.26+/-0.01 , as previously found with a different method.
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Affiliation(s)
- Eugenio Lippiello
- Istituto Nazionale di Fisica della Materia, Unità di Salerno and Dipartimento di Fisica E.R. Caianiello, Università di Salerno, 84081 Baronissi, Salerno, Italy.
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Corberi F, Castellano C, Lippiello E, Zannetti M. Generic features of the fluctuation dissipation relation in coarsening systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:017103. [PMID: 15324206 DOI: 10.1103/physreve.70.017103] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2003] [Indexed: 05/24/2023]
Abstract
The integrated response function in phase-ordering systems with scalar, vector, conserved, and nonconserved order parameter is studied at various space dimensionalities. Assuming scaling of the aging contribution chi(ag) (t, t(w) )= tw (- a(chi) ) chi; (t/ t(w) ) we obtain, by numerical simulations and analytical arguments, the phenomenological formula describing the dimensionality dependence of a(chi) in all cases considered. The primary result is that a(chi) vanishes continuously as d approaches the lower critical dimensionality d(L). This implies that (i) the existence of a nontrivial fluctuation dissipation relation and (ii) the failure of the connection between statics and dynamics are generic features of phase ordering at d(L).
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Affiliation(s)
- Federico Corberi
- Istituto Nazionale per la Fisica della Materia, Unità di Salerno and Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, 84081 Baronissi (Salerno), Italy.
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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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