A far-from-equilibrium fluctuation-dissipation relation for an Ising-Glauber-like model

Abstract

We derive an exact expression of the response function to an infinitesimal magnetic field for an Ising-Glauber-like model with arbitrary exchange couplings. The result is expressed in terms of thermodynamic averages and does not depend on the initial conditions or on the dimension of the space. The response function is related to time-derivatives of a complicated correlation function and so the expression is a generalisation of the equilibrium fluctuation-dissipation theorem in the special case of this model. Correspondence with the Ising-Glauber model is discussed. A discrete-time version of the relation is implemented in Monte Carlo simulations and then used to study the aging regime of the ferromagnetic two-dimensional Ising-Glauber model quenched from the paramagnetic phase to the ferromagnetic one. Our approach has the originality to give direct access to the response function and the fluctuation-dissipation ratio.

16 pages, 4 figures, major improvement

References in corpus (16)

• Theory of Phase Ordering Kinetics
• 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
• Fluctuation-dissipation ratio of a spin glass in the aging regime
• Response of non-equilibrium systems at criticality: Ferromagnetic models in dimension two and above
• Monte-Carlo simulations of the violation of the fluctuation-dissipation theorem in domain growth processes
• Response of non-equilibrium systems at criticality: Exact results for the Glauber-Ising chain
• Nonequilibrium critical dynamics of ferromagnetic spin systems
• Violation of the Fluctuation Dissipation Theorem in Finite Dimensional Spin Glasses
• Fluctuation dissipation ratio in the one dimensional kinetic Ising model
• Aging, phase ordering and conformal invariance
• Fluctuation Dissipation Ratio in Three-Dimensional Spin Glasses
• Slow relaxation in the large N model for phase ordering
• Two-loop Critical Fluctuation-Dissipation Ratio for the Relaxational Dynamics of the O(N) Landau-Ginzburg Hamiltonian
• Violation of the Fluctuation-Dissipation Theorem in a Two-Dimensional Ising Model with Dipolar Interactions
• Reply to a Comment

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