Critical ageing of Ising ferromagnets relaxing from an ordered state

Abstract

We investigate the nonequilibrium behavior of the d-dimensional Ising model with purely dissipative dynamics during its critical relaxation from a magnetized initial configuration. The universal scaling forms of the two-time response and correlation functions of the magnetization are derived within the field-theoretical approach and the associated scaling functions are computed up to first order in the ǫ-expansion (ǫ = 4 − d). Aging behavior is clearly displayed and the associated universal fluctuation-dissipation ratio tends to X ∞ = . The crossover to the case of relaxation from a disordered state is discussed and the crossover function for the fluctuation-dissipation ratio is computed within the Gaussian approximation.

Ageing in the contact process: scaling behaviour and universal features

“…As explained in subsection 2.1, Ξ −1 = 0 is a signal of the breaking of the RR symmetry characterizing the non-equilibrium stationary state of the CP (and of the DP universality class in general). Here we show explicitly (within the Gaussian approximation -though the conclusion is expected to be valid also beyond the approximation) that only the homogeneous fluctuation mode q = 0 is, at criticality, responsible for such a breaking, as in the case of systems with detailed balance (see, e.g, [13,20,27,30]). Indeed, let us generalize equation (15) to modes with q = 0:…”

“…Notice that we can use the O(ṽ 0 )-propagators to compute them up to O(ṽ). We first need the expressions for the following bubbles [27].) The result is The contribution I 2 is instead given by Its dimensional pole is properly removed by introducing the renormalized quantities according to equation (A.3), so that R R,q=0 = Z ψ R q=0 which gives indeed the expression in equation (30) forṽ =ṽ * R = ǫ/24 + O(ǫ 2 ).…”

“…According to the analogy discussed above one expects the following scaling form for the two-time response function in momentum space (see, e.g., [2,28] and section 3 in [27])…”

“…The analytic computation of the response function follows the same steps as those discussed in [27] (see also [25]) for the non-equilibrium relaxation of the Ising model relaxing from a state with non-vanishing value of the magnetization. Here we briefly outline the calculation.…”

On the identification of quasiprimary scaling operators in local scale-invariance

“…The scaling of two-time observables has been recently discussed in [9,10,11] and it was shown that for m 0 = 0 the universal scaling behaviour is different from the one found for m 0 = 0. An extension of LSI to non-equilibrium critical dynamics with non-vanishing initial magnetizations is an open problem to which to hope to return elsewhere.…”