Ageing in homogeneous systems at criticality

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.