Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0711.1527 · Journal of Statistical Mechanics Theory and Experiment

The non-equilibrium response of the critical Ising model: universal scaling properties and local scale invariance

Federico Corberi, Andrea Gambassi, Eugenio Lippiello, Marco Zannetti

Published Feb 27, 2008• 7 citations
arXivHTMLPDF

Abstract

Motivated by recent numerical findings of Henkel et al (2006 J. Phys. A: Math. Gen. 39 L589) we re-examine via Monte Carlo simulations the linear response function of the two-dimensional Ising model with Glauber dynamics quenched to the critical point. At variance with the results of Henkel et al , we detect discrepancies between the actual scaling behavior of the response function and the prediction of local scale invariance. Such differences are clearly visible in the impulse autoresponse function, whereas they are drastically reduced in the integrated response functions. Accordingly, the scaling form predicted on the basis of local scale invariance simply provides an accurate fitting form for some quantities but cannot be considered to be exact.

DOI
10.1088/1742-5468/2008/02/p02013

Related papers

Test of local scale invariance from the direct measurement of the response function in the Ising model quenched to and below TC

Eugenio Lippiello, Federico Corberi, Marco Zannetti

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.

arXiv:cond-mat/0604321•Physical Review E•Oct 17, 2006•24 citations

Dynamical response function of the disordered kinetic Ising model

Haye Hinrichsen B

Recently Baumann et al (2007 Preprint 0709.3228v1) studied the phase-ordering kinetics of the two-dimensional Ising model for T < T c with uniform spatially quenched disorder by Monte Carlo simulations. They found that the two-time response and correlation functions are in agreement with the predictions of local scale invariance generalized to . The present paper shows why this is actually not true and suggests an alternative approach which leads to a much better agreement with the numerical results.

arXiv:0711.2421•Journal of Statistical Mechanics Theory and Experiment•Feb 29, 2008•4 citations

Two-time autocorrelation function in phase-ordering kinetics from local scale invariance

Malte Henkel, A Picone, M Pleimling

The time-dependent scaling of the two-time autocorrelation function of spin systems without disorder undergoing phase-ordering kinetics is considered. Its form is shown to be determined by an extension of dynamical scaling to a local scale invariance which turns out to be a new version of conformal invariance. The predicted autocorrelator is in agreement with Monte Carlo data on the autocorrelation function of the 2D kinetic Ising model with Glauber dynamics quenched to a temperature below criticality.

arXiv:cond-mat/0404464•Europhysics Letters (EPL)•Oct 1, 2004•54 citations

On the identification of quasiprimary scaling operators in local scale-invariance

Malte Henkel, Tilman Enss, Michel Pleimling

The relationship between physical observables defined in lattice models and the associated (quasi-)primary scaling operators of the underlying field theory is revisited. In the context of local scale-invariance, we argue that this relationship is only defined up to a time-dependent amplitude and derive the corresponding generalizations of predictions for two-time response and correlation functions. Applications to non-equilibrium critical dynamics of several systems, with a fully disordered initial state and vanishing initial magnetization, including the Glauber–Ising model, the Frederikson–Andersen model and the Ising spin glass are discussed. The critical contact process and the parity-conserving non-equilibrium kinetic Ising model are also considered.

arXiv:cond-mat/0605211•Journal of Physics A Mathematical and General•Oct 4, 2006•40 citations

Ageing and non-equilibrium critical phenomena in Monte Carlo simulations

Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov

It is considered the non-equilibrium critical evolution of statistical systems which displays some features, such as ageing and violation of the fluctuation-dissipation theorem. We review here some theoretical results of computations that have been obtained in recent years for universal quantities, such as the exponents determining the scaling behaviour of dynamic response and correlation functions and the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the 3D pure and diluted Ising models with Glauber dynamics. We analyse an influence of critical fluctuations, different non-equilibrium initial states and presence of nonmagnetic impurities in spin systems on two-time dependence of correlation and response functions on characteristic time variables as waiting time t w and time of observation t – t w with t > t w . We discuss the obtained values of non-equilibrium exponents for autocorrelation and response functions and values of the universal long-time limit of the fluctuation-dissipation ratio X ∞ . Analysis of simulation results show that the insertion of disorder leads to new values of X ∞ with X ∞ diluted > X ∞ pure .

Journal of Physics Conference Series•May 15, 2014•2 citations

Response of non-equilibrium systems at criticality: ferromagnetic models in dimension two and above

Claude Godrèche, J. M. Luck

We study the dynamics of ferromagnetic spin systems quenched from infinite temperature to their critical point. We perform an exact analysis of the spherical model in any dimension D >2 and numerical simulations on the two-dimensional Ising model. These systems are shown to be ageing in the long-time regime, i.e. their two-time autocorrelation and response functions, and associated fluctuation-dissipation ratio, are non-trivial scaling functions of both time variables. We show in particular that, for 1<< s (waiting time) << t (observation time), the fluctuation-dissipation ratio possesses a non-trivial limit value X ∞ , which appears as a dimensionless amplitude ratio, and is therefore a novel universal characteristic of non-equilibrium critical dynamics. For the spherical model, we obtain X ∞ = 1-2/ D for 2< D <4 and X ∞ = ½ for D >4 (mean-field regime). For the two-dimensional Ising model we measure X ∞ ≈0.26±0.01.

arXiv:cond-mat/0001264•Journal of Physics A Mathematical and General•Dec 7, 2000•183 citations
Motivated by recent numerical findings of Henkel et al (2006 J. Phys. A: Math. Gen. 39 L589) we re-examine via Monte Carlo simulations the linear response function of the two-dimensional Ising model with Glauber dynamics quenched to the critical point. At variance with the results of Henkel et al , we detect discrepancies between the actual scaling behavior of the response function and the prediction of local scale invariance. Such differences are clearly visible in the impulse autoresponse function, whereas they are drastically reduced in the integrated response functions. Accordingly, the scaling form predicted on the basis of local scale invariance simply provides an accurate fitting form for some quantities but cannot be considered to be exact.
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.
Recently Baumann et al (2007 Preprint 0709.3228v1) studied the phase-ordering kinetics of the two-dimensional Ising model for T < T c with uniform spatially quenched disorder by Monte Carlo simulations. They found that the two-time response and correlation functions are in agreement with the predictions of local scale invariance generalized to . The present paper shows why this is actually not true and suggests an alternative approach which leads to a much better agreement with the numerical results.
The time-dependent scaling of the two-time autocorrelation function of spin systems without disorder undergoing phase-ordering kinetics is considered. Its form is shown to be determined by an extension of dynamical scaling to a local scale invariance which turns out to be a new version of conformal invariance. The predicted autocorrelator is in agreement with Monte Carlo data on the autocorrelation function of the 2D kinetic Ising model with Glauber dynamics quenched to a temperature below criticality.
The relationship between physical observables defined in lattice models and the associated (quasi-)primary scaling operators of the underlying field theory is revisited. In the context of local scale-invariance, we argue that this relationship is only defined up to a time-dependent amplitude and derive the corresponding generalizations of predictions for two-time response and correlation functions. Applications to non-equilibrium critical dynamics of several systems, with a fully disordered initial state and vanishing initial magnetization, including the Glauber–Ising model, the Frederikson–Andersen model and the Ising spin glass are discussed. The critical contact process and the parity-conserving non-equilibrium kinetic Ising model are also considered.
It is considered the non-equilibrium critical evolution of statistical systems which displays some features, such as ageing and violation of the fluctuation-dissipation theorem. We review here some theoretical results of computations that have been obtained in recent years for universal quantities, such as the exponents determining the scaling behaviour of dynamic response and correlation functions and the fluctuation-dissipation ratio, associated with the non-equilibrium critical dynamics, with particular focus on the 3D pure and diluted Ising models with Glauber dynamics. We analyse an influence of critical fluctuations, different non-equilibrium initial states and presence of nonmagnetic impurities in spin systems on two-time dependence of correlation and response functions on characteristic time variables as waiting time t w and time of observation t – t w with t > t w . We discuss the obtained values of non-equilibrium exponents for autocorrelation and response functions and values of the universal long-time limit of the fluctuation-dissipation ratio X ∞ . Analysis of simulation results show that the insertion of disorder leads to new values of X ∞ with X ∞ diluted > X ∞ pure .
We study the dynamics of ferromagnetic spin systems quenched from infinite temperature to their critical point. We perform an exact analysis of the spherical model in any dimension D >2 and numerical simulations on the two-dimensional Ising model. These systems are shown to be ageing in the long-time regime, i.e. their two-time autocorrelation and response functions, and associated fluctuation-dissipation ratio, are non-trivial scaling functions of both time variables. We show in particular that, for 1<< s (waiting time) << t (observation time), the fluctuation-dissipation ratio possesses a non-trivial limit value X ∞ , which appears as a dimensionless amplitude ratio, and is therefore a novel universal characteristic of non-equilibrium critical dynamics. For the spherical model, we obtain X ∞ = 1-2/ D for 2< D <4 and X ∞ = ½ for D >4 (mean-field regime). For the two-dimensional Ising model we measure X ∞ ≈0.26±0.01.