Ageing in the critical contact process: a Monte Carlo study

TL;DR

This study investigates the aging dynamics of the critical contact process using Monte Carlo simulations and mean-field theory, revealing broken time-translation invariance and distinct aging exponents, challenging the applicability of non-equilibrium temperature concepts.

Contribution

It provides the first detailed analysis of aging phenomena in the critical contact process, demonstrating broken time-translation invariance and differences in aging exponents.

Findings

Time-translation invariance is broken during aging.

Autocorrelation and autoresponse exponents are equal.

A non-equilibrium temperature concept is not applicable.

Abstract

The long-time dynamics of the critical contact process which is brought suddenly out of an uncorrelated initial state undergoes ageing in close analogy with quenched magnetic systems. In particular, we show through Monte Carlo simulations in one and two dimensions and through mean-field theory that time-translation invariance is broken and that dynamical scaling holds. We find that the autocorrelation and autoresponse exponents lambda_{Gamma} and lambda_R are equal but, in contrast to systems relaxing to equilibrium, the ageing exponents a and b are distinct. A recent proposal to define a non-equilibrium temperature through the short-time limit of the fluctuation-dissipation ratio is therefore not applicable.