Fluctuations and effective temperatures in coarsening

Abstract

We study dynamic fluctuations in non-disordered finite dimensional ferromagnetic systems quenched to the critical point and the low-temperature phase. We investigate the fluctuations of two two-time quantities, called χ and C, the averages of which yield the self linear response and correlation function. We introduce a restricted average of the χ's, summing over all configurations with a given value of C. We find that the restricted average χ C obeys a scaling form, and that the slope of the scaling function approaches the universal value X∞ of the limiting effective temperature in the long-time limit and for C → 0. Our results tend to confirm the expectation that time-reparametrization invariance is not realized in coarsening systems at criticality. Finally, we discuss possible experimental tests of our proposal.

Fluctuations of two-time quantities and non-linear response functions

“…This mechanism makes lim tw →∞ lim t→∞ V C k=0 (t, t w ) = ∞, and in this sense the limit ( 22) is recovered, bearing in mind that ξ = ∞. Moreover, lim tw→∞ lim t→∞ V Cχ k=0 (t, t w )/V C k=0 (t, t w ), is a t w -independent constant as was found in [21]. We also observe that V Cχ k=0 going to a constant value is a different behavior with respect to the spherical model [22], where this quantity vanishes for t → ∞.…”

“…(58) or Eq. (61)) this implies that the fluctuations χ and C cannot be constrained to follow the χ(C) curve, at least in this particular order of the large time limits, as already noticed in [21]. Hence the interpretation of [18,19] cannot be strictly obeyed.…”

“…For V C k=0 (∞) and V χ k=0 (∞) the same result holds true also below (but close to) T c , since the terms containing the magnetization in Eqs. (21) can be neglected. Interestingly, the behavior of V Cχ k=0 (∞), on the other hand, is discontinuous around the critical temperature: It vanishes identically for T > T c while it diverges as −(T c − T ) 2β−γ (where γ = (2 − η)ν and β are the usual critical exponents) on approaching T c from below.…”

Fluctuations of two-time quantities and time-reparameterization invariance in spin glasses

“…For a generic fluctuating observable X, besides the standard full average X = X we also introduce the restricted average X C = X C , namely an average taken only over the instances (realizations) with a given value C of the fluctuating autocorrelation, as suggested in [16]. Clearly one has…”

Domain growth and aging scaling in coarsening disordered systems

“…In this context the theoretical study of perfect, i.e. nondisordered, models has been most fruitful, see, for example, [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22].…”