Novel Position-Space Renormalization Group for Bond Directed Percolation in Two Dimensions

TL;DR

This paper introduces a novel position-space renormalization group method for two-dimensional bond directed percolation, accurately estimating the critical threshold and correlation length exponents, aligning well with existing series expansion results.

Contribution

It presents a new RG approach specifically tailored for bond directed percolation in two dimensions, providing precise estimates of critical parameters.

Findings

Critical threshold p_c=0.6443

Correlation length exponents ν_∥=1.719 and ν_⊥=1.076

Results agree with best known series expansion data

Abstract

A new position-space renormalization group approach is investigated for bond directed percolation in two dimensions. The threshold value for the bond occupation probabilities is found to be $p_c=0.6443$. Correlation length exponents on time (parallel) and space (transverse) directions are found to be $\nu_\parallel=1.719$ and $\nu_\perp=1.076$, respectively, which are in very good agreement with the best known series expansion results.