Precise calculation of the threshold of various directed percolation models on a square lattice

TL;DR

This paper uses Monte Carlo simulations to precisely determine the critical thresholds of directed percolation models on a square lattice, revealing an exponential decay related to connectivity.

Contribution

It provides highly accurate threshold values and proposes a conjecture that the critical probability decays inversely with the coordination number.

Findings

Critical thresholds decrease exponentially with connectivity.

Conjecture that $p_{c}$ decays as the inverse of the coordination number.

High-precision threshold values for various models.

Abstract

Using Monte Carlo simulations on different system sizes we determine with high precision the critical thresholds of two families of directed percolation models on a square lattice. The thresholds decrease exponentially with the degree of connectivity. We conjecture that $p_{c}$ decays exactly as the inverse of the coodination number.