Universality classes for percolation models with long-range correlations

TL;DR

This paper studies percolation models with long-range correlations decaying as a power law, providing analytical and simulation results that identify universal critical exponents depending only on the decay parameter and dimension.

Contribution

It introduces a class of correlated percolation models and derives universal critical exponents as rational functions of decay and dimension parameters.

Findings

Critical exponents are rational functions of parameters a and d.

Analytical results match simulation data.

Critical behavior is universal across models with similar decay properties.

Abstract

We consider a class of percolation models where the local occupation variables have long-range correlations decaying as a power law $\sim r^{-a}$ at large distances $r$, for some $0< a< d$ where $d$ is the underlying spatial dimension. For several of these models, we present both, rigorous analytical results and matching simulations that determine the critical exponents characterizing the fixed point associated to their phase transition, which is of second order. The exact values we obtain are rational functions of the two parameters $a$ and $d$ alone, and do not depend on the specifics of the model.