Ageing in the contact process: Scaling behavior and universal features

TL;DR

This paper studies the aging phenomena in the contact process at criticality, analyzing the scaling of response and correlation functions, and compares theoretical predictions with numerical results.

Contribution

It provides a field-theoretical calculation of the two-time response function and its universal ratio, revealing deviations from local scale invariance predictions.

Findings

Response function scaling does not match local scale invariance theory.

Universal ratio of response to correlation functions calculated up to first order.

Qualitative agreement with recent numerical simulations.

Abstract

We investigate some aspects of the ageing behavior observed in the contact process after a quench from its active phase to the critical point. In particular we discuss the scaling properties of the two-time response function and we calculate it and its universal ratio to the two-time correlation function up to first order in the field-theoretical epsilon-expansion. The scaling form of the response function does not fit the prediction of the theory of local scale invariance. Our findings are in good qualitative agreement with recent numerical results.