Comparative study of spanning cluster distributions in different dimensions

TL;DR

This study analyzes how the distributions of spanning cluster masses in percolation lattices vary across dimensions 2 to 5, revealing simple power law relationships and differences in multiple spanning cluster cases.

Contribution

It provides a comprehensive comparison of spanning cluster distributions across multiple dimensions and discusses the behavior of multiple spanning clusters.

Findings

Cumulants and exponents follow power law variations with dimension.

Universal scaling functions exhibit simple power law behavior.

Multiple spanning cluster cases show distinct characteristics.

Abstract

The probability distributions of the masses of the clusters spanning from top to bottom of a percolating lattice at the percolation threshold are obtained in all dimensions from two to five. The first two cumulants and the exponents for the universal scaling functions are shown to have simple power law variations with the dimensionality. The cases where multiple spanning clusters occur are discussed separately and compared.