Low-density series expansions for directed percolation IV. Temporal disorder

TL;DR

This paper develops a model for temporally disordered directed percolation, calculates low-density series, and analyzes critical parameters, revealing continuous changes with disorder strength.

Contribution

It introduces a new model for temporally disordered directed percolation and provides efficient series calculations and analysis of critical behavior.

Findings

Critical point estimates vary with disorder strength

Critical exponents show continuous change with disorder

Series analysis confirms continuous phase transition behavior

Abstract

We introduce a model for temporally disordered directed percolation in which the probability of spreading from a vertex $(t,x)$, where $t$ is the time and $x$ is the spatial coordinate, is independent of $x$ but depends on $t$. Using a very efficient algorithm we calculate low-density series for bond percolation on the directed square lattice. Analysis of the series yields estimates for the critical point $p_c$ and various critical exponents which are consistent with a continuous change of the critical parameters as the strength of the disorder is increased.