Are the Tails of Percolation Thresholds Gaussians ?

TL;DR

This paper investigates the distribution of percolation thresholds in finite lattices, challenging previous beliefs about their statistical nature and providing new evidence that the question remains unresolved.

Contribution

It presents improved Monte Carlo data that questions the assumed Gaussian or stretched exponential distributions of percolation thresholds.

Findings

Evidence against the Gaussian distribution of thresholds

Indications that the distribution behavior is still uncertain

Enhanced simulation data for future analysis

Abstract

The probability distribution of percolation thresholds in finite lattices were first believed to follow a normal Gaussian behaviour. With increasing computer power and more efficient simulational techniques, this belief turned to a stretched exponential behaviour, instead. Here, based on a further improvement of Monte Carlo data, we show evidences that this question is not yet answered at all.