# Contact process with aperiodic temporal disorder

## TL;DR

This paper studies how deterministic aperiodic temporal disorder affects the critical behavior of the contact process, using analytic and numerical methods to test a generalized relevance criterion.

## Contribution

It introduces a framework to analyze the impact of aperiodic temporal disorder on nonequilibrium phase transitions, extending the relevance criterion to these systems.

## Key findings

- The generalized criterion is validated in the mean-field limit.
- Temporal disorder influences the critical behavior depending on the wandering exponent.
- Analytic and numerical results support the relevance of aperiodic sequences in nonequilibrium models.

## Abstract

We investigate the nonequilibrium critical behavior of the contact process with deterministic aperiodic temporal disorder implemented by choosing healing or infection rates according to a family of aperiodic sequences based on the quasiperiodic Fibonacci sequence. This family allows us to gauge the temporal fluctuations via a wandering exponent $\omega$ and put our work in the context of the Kinzel--Vojta--Dickman criterion for the relevance of temporal disorder to the critical behavior of nonequilibrium models. By means of analytic and numerical calculations, the generalized criterion is tested in the mean-field limit.