Correlation Length Exponent in the Three-Dimensional Fuse Network

TL;DR

This paper numerically measures the correlation length exponent in a 3D fuse model, finding it close to the percolation value, suggesting they share the same universality class.

Contribution

The study provides the first numerical estimate of the correlation length exponent in the 3D fuse model, linking it to percolation universality.

Findings

The correlation length exponent nu is approximately 0.86.

The exponent value is close to the percolation value of 0.88.

The 3D fuse model likely belongs to the percolation universality class.

Abstract

We present numerical measurements of the critical correlation length exponent nu in the three-dimensional fuse model. Using sufficiently broad threshold distributions to ensure that the system is the strong-disorder regime, we determine nu to be nu = 0.86 +/- 0.06 based on analyzing the fluctuations of the survival probability. The value we find for nu is very close to the percolation value 0.88 and we propose that the three-dimensional fuse model is in the universality class of ordinary percolation.