Low-density series expansions for directed percolation III. Some two-dimensional lattices

TL;DR

This paper computes low-density series expansions for directed percolation on various 2D lattices, providing precise estimates of critical points and exponents, supporting universality in directed percolation.

Contribution

It introduces efficient algorithms for calculating series on multiple lattices and offers high-precision estimates of critical parameters, confirming universality of critical exponents.

Findings

Critical point estimates with high accuracy

Critical exponents consistent across lattices

Analysis of non-physical singularities

Abstract

We use very efficient algorithms to calculate low-density series for bond and site percolation on the directed triangular, honeycomb, kagom\'e, and $(4.8^2)$ lattices. Analysis of the series yields accurate estimates of the critical point $p_c$ and various critical exponents. The exponent estimates differ only in the $5^{th}$ digit, thus providing strong numerical evidence for the expected universality of the critical exponents for directed percolation problems. In addition we also study the non-physical singularities of the series.