Ageing in homogeneous systems at criticality

TL;DR

This paper investigates ageing phenomena in homogeneous critical systems, demonstrating that the usual separation of dynamical regimes does not apply and analyzing conditions for the equality of specific ageing exponents.

Contribution

It challenges the common belief that homogeneous critical systems have distinct quasi-stationary and ageing regimes, showing that the two limits commute and examining exponent relations.

Findings

The two limits of response functions commute in homogeneous critical systems.

Homogeneous critical systems lack a separate quasi-stationary regime.

Conditions for the equality of ageing exponents a and a' are discussed.

Abstract

Ageing phenomena are observed in a large variety of dynamical systems exhibiting a slow relaxation from a non-equilibrium initial state. Ageing can be characterised in terms of the linear response R(t,s) at time t to a local perturbation at time s<t. Usually one distinguishes two dynamical regimes, namely, the quasi-stationary regime, where the response is translationally invariant in time, and the ageing regime, where this invariance is broken. In general these two regimes are separate in the sense that the two limits of (a) taking t,s to infinity while keeping t/s fixed, and (b) taking t,s to infinity with fixed t-s, give different results. In recent years, ageing was also investigated in the context of homogeneous critical systems such as the Glauber-Ising model and the contact process. Here we argue that, in contrast to a widespread believe, homogeneous critical systems do not have a separate quasi-stationary regime, hence the two limits do commute. Moreover, it is discussed under which conditions two particular exponents, denoted as a and a' in the literature, have to be identical.