Disordered contact process with asymmetric spreading

TL;DR

This paper introduces an asymmetric contact process model with independent spreading rates, analyzing how local asymmetry affects large-scale behavior and phase transitions, revealing different universality classes depending on global bias.

Contribution

It develops a real space renormalization scheme for the asymmetric contact process and shows the irrelevance of local asymmetry under global symmetry, identifying distinct phase transitions.

Findings

Local asymmetry is irrelevant under global symmetry.

Two distinct phase transitions are predicted with global bias.

Spreading against the bias is governed by an infinite randomness fixed point.

Abstract

An asymmetric variant of the contact process where the activity spreads with different and independent random rates to the left and to the right is introduced. A real space renormalization scheme is formulated for model by means of which it is shown that the local asymmetry of spreading is irrelevant on large scales if the model is globally (statistically) symmetric. Otherwise, in the presence of a global bias in either direction, the renormalization method predicts two distinct phase transitions, which are related to the spreading of activity in and against the direction of the bias. The latter is found to be described by an infinite randomness fixed point while the former is not.