The fluctuation-dissipation relation in an Ising model without detailed balance

Abstract

We consider the modified Ising model introduced by de Oliveira et al. [J.Phys.A {\bf 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 which 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 non-stationary phase ordering kinetics the parametric plot of the integrated response function $\chi (t,t_w)$ versus 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 ${\chi }_{ag}(t,t_w)\sim t_w^{-a_{\chi }}f(t/t_w)$, and a numerical value of $a_{\chi }$ consistent with $a_{\chi }=1/4$, as in the kinetic Ising model.

arXiv comment17 pages, 15 figures. To appear on Physical Review E

References in corpus (21)

• Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
• Energy flow, partial equilibration and effective temperatures in systems with slow dynamics
• On the Out of Equilibrium Relaxation of the Sherrington - Kirkpatrick model
• Violation of the fluctuation-dissipation theorem in glassy systems: basic notions and the numerical evidence
• Measuring equilibrium properties in aging systems
• Off equilibrium dynamics and aging in unfrustrated systems
• Weak-ergodicity breaking in mean-field spin-glass models
• The response of glassy systems to random perturbations: A bridge between equilibrium and off-equilibrium
• Off-equilibrium generalization of the fluctuation dissipation theorem for Ising spins and measurement of the linear response function
• A far-from-equilibrium fluctuation-dissipation relation for an Ising-Glauber-like model
• On the connection between off-equilibrium response and statics in non disordered coarsening systems
• Coarsening and persistence in a class of stochastic processes interpolating between the Ising and voter models
• Interface fluctuations, bulk fluctuations and dimensionality in the off-equilibrium response of coarsening systems
• Scaling of the linear response function from zero field cooled and thermoremanent magnetization in phase ordering kinetics
• Bona Fide Thermodynamic Temperature in Nonequilibrium Kinetic Ising Models
• Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems
• Generic features of the fluctuation dissipation relation in coarsening systems
• Comment on "Aging, phase ordering and conformal invariance"
• Correlation Functions and Fluctuation-Dissipation Relation in Driven Mixtures: an exactly solvable model
• Effects of an external drive on the fluctuation-dissipation relation of phase-ordering systems
• Comment on "Scaling of the linear response in simple aging systems without disorder"

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• Fluctuations of two-time quantities and time-reparametrization invariance in spin-glasses
• Ageing in bosonic particle-reaction models with long-range transport
• Heat fluctuations in Ising models coupled with two different heat baths
• Stationarization and Multithermalization in spin glasses
• Fluctuation relations in non-equilibrium stationary states of Ising models
• Entropy-based characterizations of the observable-dependence of the fluctuation-dissipation temperature
• Relaxation processes in a system with logarithmic growth
• Heat exchanges in coarsening systems
• Aging and stationary properties of non-equilibrium symmetrical three-state models
• Thermalization with a multibath: an investigation in simple models