Ageing phenomena without detailed balance: the contact process

TL;DR

This paper investigates the ageing dynamics of the 1D contact process at criticality using a light-cone transfer-matrix renormalisation group, revealing non-equilibrium scaling behaviors and confirming local scale-invariance predictions.

Contribution

It provides a detailed analysis of ageing phenomena without detailed balance in the contact process, highlighting non-trivial scaling and fluctuation-dissipation properties.

Findings

Ageing exponents a and b are unequal, indicating no finite fluctuation-dissipation ratio.

Critical autoresponse function scaling matches local scale-invariance predictions.

Ageing dynamics characterized by non-equilibrium scaling laws in the contact process.

Abstract

The long-time dynamics of the 1D contact process suddenly brought out of an uncorrelated initial state is studied through a light-cone transfer-matrix renormalisation group approach. At criticality, the system undergoes ageing which is characterised through the dynamical scaling of the two-times autocorrelation and autoresponse functions. The observed non-equality of the ageing exponents a and b excludes the possibility of a finite fluctuation-dissipation ratio in the ageing regime. The scaling form of the critical autoresponse function is in agreement with the prediction of local scale-invariance.