Wrapping probabilities for Potts spin clusters on a torus

TL;DR

This paper derives and tests formulas for wrapping probabilities of Ising and Potts spin clusters on a torus, providing new analytical results and numerical validation for these topological probabilities.

Contribution

It introduces new formulas for wrapping probabilities of Potts and Ising clusters on a torus, including cross clusters, with validation through simulations.

Findings

Derived analytical formulas for wrapping probabilities

Validated formulas with numerical simulations

Provided closed-form expressions for cross cluster probabilities

Abstract

In this work we obtain wrapping probabilities for Ising spin clusters on a torus. We use the analogy with the tricritical point of a Potts model with dilution. The formula obtained are tested against numerical simulation. We also provide closed form for the wrapping probabilities of cross clusters on untwisted tori.