Comment on: "Superscaling of Percolation on Rectangular Domains"

TL;DR

This paper critiques a previous study on superscaling in 2D percolation, highlighting issues with the proposed scaling ansatz and explaining why these were not evident in earlier numerical results.

Contribution

It provides a critical analysis of the superscaling hypothesis, identifying potential flaws and offering insights into the limitations of the original numerical approach.

Findings

Identifies difficulties with the superscaling ansatz

Explains why the issues were not detected in prior analysis

Suggests the need for revised scaling considerations

Abstract

In [Watanabe et al., Phys. Rev. Lett. 93 190601 (2004)], the authors show numerically that spanning and percolation probabilities in two-dimensional systems with different aspect ratios obey a form of "superscaling". In this comment, we would like to point out some difficulties with their proposed scaling ansatz and suggest why this remained undetected in their numerical analysis.