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Off-equilibrium generalization of the fluctuation dissipation theorem for Ising spins and measurement of the linear response function

Eugenio Lippiello^*, Federico Corberi^†, and Marco Zannetti^‡

Istituto Nazionale di Fisica della Materia, Unità di Salerno and Dipartimento di Fisica “E.R. Caianiello,” Università di Salerno, 84081 Baronissi (Salerno), Italy

^*Email address: lippiello@sa.infn.it
^†Email address: corberi@sa.infn.it
^‡Email address: zannetti@na.infn.it

Phys. Rev. E 71, 036104 – Published 7 March, 2005

DOI: https://doi.org/10.1103/PhysRevE.71.036104

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 $χ (t, t_{w}) ≃ t_{w}^{- a} f (t ∕ t_{w})$ , with $a = 0.26 \pm 0.01$ , as previously found with a different method.

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References (24)

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Off-equilibrium generalization of the fluctuation dissipation theorem for Ising spins and measurement of the linear response function

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