Winding clusters in percolation on the Torus and the Moebius strip

TL;DR

This paper uses advanced simulation techniques to study winding clusters in percolation on the torus and Moebius strip, providing high-accuracy results that align with conformal field theory predictions and highlighting new phenomena for future theoretical analysis.

Contribution

It introduces a novel simulation approach enabling large-scale studies of winding clusters in complex topologies, with results consistent with theoretical predictions and revealing new questions.

Findings

Results align with conformal field theory predictions

First large-scale simulation study of winding clusters on these topologies

Numerical data for Moebius strip and winding cluster distribution

Abstract

Using a simulation technique introduced recently, we study winding clusters in percolation on the torus and the Moebius strip for different aspect ratios. The asynchronous parallelization of the simulation makes very large system and sample sizes possible. Our high accuracy results are fully consistent with predictions from conformal field theory. The numerical results for the Moebius strip and the number distribution of winding clusters on the torus await theoretical explanation. To our knowledge, this study is the first of its kind.