Corrections to local scale invariance in the non-equilibrium dynamics of critical systems: numerical evidences

Local scale invariance (LSI) has been recently proposed as a possible extension of the dynamical scaling in systems at the critical point and during phase ordering. LSI has been applied inter alia to provide predictions for the scaling properties of the response function of non-equilibrium critical systems in the aging regime following a quench from the high-temperature phase to the critical point. These predictions have been confirmed by Monte Carlo simulations and analytical results for some specific models, but they are in disagreement with field-theoretical predictions. By means of Monte Carlo simulations of the critical two- and three-dimensional Ising model with Glauber dynamics, we study the intermediate integrated response, finding deviations from the corresponding LSI predictions that are in qualitative agreement with the field-theoretical computations. This result casts some doubts on the general applicability of LSI to critical dynamics.Comment: 4 pages, 2 figures, minor changes, version to appear in Phys. Rev. B as a Rapid Communicatio

Hilbert Space Representation of an Algebra of Observables for q-Deformed Relativistic Quantum Mechanics

Using a representation of the q-deformed Lorentz algebra as differential operators on quantum Minkowski space, we define an algebra of observables for a q-deformed relativistic quantum mechanics with spin zero. We construct a Hilbert space representation of this algebra in which the square of the mass $p^2$ is diagonal.Comment: 13 pages, LMU-TPW 94-

Scaling of the linear response in simple ageing systems without disorder

The time-dependent scaling of the thermoremanent and zero-field-cooled susceptiblities in ferromagnetic spin systems undergoing ageing 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 $\chi_{\rm FC}(t)-\chi_0\sim t^{-A}$ 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 $\chi_{\rm ZFC}(t,s)$, but does not enter into the thermoremanent susceptibility $\rho_{\rm TRM}(t,s)$. However, there may be large finite-time corrections to the scaling of $\rho_{\rm TRM}(t,s)$ which are explicitly derived and may be needed in order to extract reliable ageing exponents. Consistency with the predictions of local scale invariance is confirmed in the Glauber-Ising and spherical models.Comment: Latex2e, 14 pages, with 6 figure

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

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.Comment: Latex2e, 7 pages with 2 figures, with epl macro, final from, to appear in EP

Is local scale invariance a generic property of ageing phenomena ?

In contrast to recent claims by Enss, Henkel, Picone, and Schollwoeck [J. Phys. A 37, 10479] it is shown that the critical autoresponse function of the 1+1-dimensional contact process is not in agreement with the predictions of local scale invariance.Comment: 7 pages, 3 figures, final form, c++ source code on reques

Dynamics of dilute disordered models: a solvable case

We study the dynamics of a dilute spherical model with two body interactions and random exchanges. We analyze the Langevin equations and we introduce a functional variational method to study generic dilute disordered models. A crossover temperature replaces the dynamic transition of the fully-connected limit. There are two asymptotic regimes, one determined by the central band of the spectral density of the interactions and a slower one determined by localized configurations on sites with high connectivity. We confront the behavior of this model to the one of real glasses.Comment: 7 pages, 4 figures. Clarified, final versio

Scaling of the magnetic linear response in phase-ordering kinetics

The scaling of the thermoremanent magnetization and of the dissipative part of the non-equilibrium magnetic susceptibility is analysed as a function of the waiting-time $s$ for a simple ferromagnet undergoing phase-ordering kinetics after a quench into the ferromagnetically ordered phase. Their scaling forms describe the cross-over between two power-law regimes governed by the non-equilibrium exponents $a$ and $\lambda_R/z$, respectively. A relation between $a$, the dynamical exponent $z$ and the equilibrium exponent $\eta$ is derived from scaling arguments. Explicit tests in the Glauber-Ising model and the kinetic spherical model are presented.Comment: 7 pages, 2 figures included, needs epl.cls, version to appear in Europhys. Let

Superuniversality in phase-ordering disordered ferromagnets

The phase-ordering kinetics of the ferromagnetic two-dimensional Ising model with uniform bond disorder is investigated by intensive Monte Carlo simulations. Simple ageing behaviour is observed in the single-time correlator and the two-time responses and correlators. The dynamical exponent z and the autocorrelation exponent lambda_C only depend on the ratio eps/T, where eps describes the width of the distribution of the disorder, whereas a more complicated behaviour is found for the non-equilibrium exponent a of the two-time response as well as for the autoresponse exponent lambda_R. The scaling functions are observed to depend only on the dimensionless ratio eps/T. If the length scales are measured in terms of the time-dependent domain size L(t), the form of the scaling functions is in general independent of both eps and T. Conditions limiting the validity of this `superuniversality' are discussed.Comment: Latex2e, 10pp with 8 figures included, PR macro

Irreversible spherical model and its stationary entropy production rate

The nonequilibrium stationary state of an irreversible spherical model is investigated on hypercubic lattices. The model is defined by Langevin equations similar to the reversible case, but with asymmetric transition rates. In spite of being irreversible, we have succeeded in finding an explicit form for the stationary probability distribution, which turns out to be of the Boltzmann-Gibbs type. This enables one to evaluate the exact form of the entropy production rate at the stationary state, which is non-zero if the dynamical rules of the transition rates are asymmetric

Crossover from stationary to aging regime in glassy dynamics

We study the non-equilibrium dynamics of the spherical p-spin models in the scaling regime near the plateau and derive the corresponding scaling functions for the correlators. Our main result is that the matching between different time regimes fixes the aging function in the aging regime to $h(t)=\exp(t^{1-\mu})$. The exponent $\mu$ is related to the one giving the length of the plateau. Interestingly $1-\mu$ is quickly very small when one goes away from the dynamic transition temperature in the glassy phase. This gives new light on the interpretation of experiments and simulations where simple aging was found to be a reasonable but not perfect approximation, which could be attributed to the existence of a small but non-zero stretching exponent.Comment: 7 pages+2 figure