Crossover properties from random percolation to frustrated percolation

TL;DR

This study explores how the critical behavior of a frustrated percolation model on a 2D lattice transitions from standard percolation to a frustrated state as the density of antiferromagnetic interactions increases, revealing a crossover in critical exponents.

Contribution

It provides the first detailed analysis of the crossover in critical exponents from random to frustrated percolation in a 2D lattice model with asymmetric interactions.

Findings

Critical exponents vary with antiferromagnetic interaction density

Crossover from random to frustrated percolation behavior observed

Critical exponents align with the 1/2-state Potts model for pi>0

Abstract

We investigate the crossover properties of the frustrated percolation model on a two-dimensional square lattice, with asymmetric distribution of ferromagnetic and antiferromagnetic interactions. We determine the critical exponents nu, gamma and beta of the percolation transition of the model, for various values of the density of antiferromagnetic interactions pi in the range 0<pi<0.5. Our data are consistent with the existence of a crossover from random percolation behavior for pi=0, to frustrated percolation behavior, characterized by the critical exponents of the ferromagnetic 1/2-state Potts model, as soon as pi>0.