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

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 chi (t, t(w)) approximately equal to t(-a)(w) f (t/t(w)) , with a =0.26+/-0.01 , as previously found with a different method.

Role of initial state and final quench temperature on aging properties in phase-ordering kinetics

“…(13,14)]. This determination of λ χ is definitely different from the one found in previous studies [7][8][9] which were focused on quenches to final T f . Since the final temperature of the quench is expected to be an irrelevant parameter [5,10], in the sense of the renormalization group, we conjecture that λ χ = different value [11] when the quench is made from T i = ∞ [λ C (T i = ∞) = 5/4] or T i = T c [λ C (T i = T c ) 1/8], the response function exponent remains basically unchanged.…”

“…Also for these quantities the data collapse expected on the basis of the scalings (8,17) are not observed in the range of times accessed in our simulations due to important pre-asymptotic effects. .…”

“…(12)]. We obtain this quantity using the generalization to non-equilibrium states of the fluctuation-dissipation theorem derived in [8,16]. Similarly to the well known equilibrium theorem, this amounts to an analytical relation between χ and certain correlation functions of the unperturbed system, namely the one where the perturbation h is absent.…”

Scaling and universality in the aging kinetics of the two-dimensional clock model

“…In the following we will use the one derived in [12]. For spin systems subjected to a Markovian dynamics an out of equilibrium generalization of the fluctuation dissipation theorem was derived [13], relating the response functions to particular correlation functions of the unperturbed system.…”

“…In this equation [σ] and [σ ′ ] are two configurations differing only by the spin on site i, taking the values σ i and σ (11) allows to compute the integrated response function by measuring correlation functions on the unperturbed system, avoiding the complications of the traditional methods where a perturbation is applied, and improving significantly the quality of the results [12].…”