Numerical Study of a Field Theory for Directed Percolation

TL;DR

This paper introduces a numerical approach for analyzing stochastic PDEs related to directed percolation, accurately estimating critical exponents near phase transitions in 1+1 dimensions.

Contribution

It develops a discretization-based numerical method tailored for stochastic PDEs with multiplicative noise, improving analysis of directed percolation models.

Findings

Critical exponents match accepted values

Method effectively captures fluctuations near absorbing states

Applicable to models with continuous phase transitions

Abstract

A numerical method is devised for study of stochastic partial differential equations describing directed percolation, the contact process, and other models with a continuous transition to an absorbing state. Owing to the heightened sensitivity to fluctuationsattending multiplicative noise in the vicinity of an absorbing state, a useful method requires discretization of the field variable as well as of space and time. When applied to the field theory for directed percolation in 1+1 dimensions, the method yields critical exponents which compare well against accepted values.