A precise approximation for directed percolation in d=1+1

TL;DR

This paper introduces a new approximation for 1+1 dimensional directed percolation, accurately estimating the critical exponent for the order parameter, closely matching numerical results.

Contribution

It presents a novel approximation method specifically for a continuous model of directed percolation in 1+1 dimensions, providing precise critical exponent estimates.

Findings

Critical exponent beta estimated as 0.276393202...

Approximation closely matches numerical estimates

Provides a new analytical approach for directed percolation

Abstract

We introduce an approximation specific to a continuous model for directed percolation, which is strictly equivalent to 1+1 dimensional directed bond percolation. We find that the critical exponent associated to the order parameter (percolation probability) is beta=(1-1/\sqrt{5})/2=0.276393202..., in remarkable agreement with the best current numerical estimate beta=0.276486(8).