Fermionic field theory for directed percolation in (1+1) dimensions

TL;DR

This paper develops a fermionic field theory approach to analyze directed percolation in (1+1) dimensions, providing new analytical tools and estimates for critical exponents in low-dimensional systems.

Contribution

It introduces a novel fermionic field theory formulation for directed percolation, offering an alternative systematic analytical method for low-dimensional cases.

Findings

Numerical estimates for critical exponents obtained.

New fermionic field theory framework established.

Renormalization group analysis applied successfully.

Abstract

We formulate directed percolation in (1+1) dimensions in the language of a reaction-diffusion process with exclusion taking place in one space dimension. We map the master equation that describes the dynamics of the system onto a quantum spin chain problem. From there we build an interacting fermionic field theory of a new type. We study the resulting theory using renormalization group techniques. This yields numerical estimates for the critical exponents and provides a new alternative analytic systematic procedure to study low-dimensional directed percolation.