Avalanche size distribution in the Toom interface

TL;DR

This paper investigates the avalanche size distribution and height correlations in the 3D Toom interface, revealing exponential decay in avalanche sizes and logarithmic divergence in height fluctuations, with a generalization to arbitrary dimensions.

Contribution

It provides numerical analysis of avalanche distributions and height correlations in the 3D Toom interface, highlighting differences from typical critical phenomena and extending the model to higher dimensions.

Findings

Avalanche size distribution decays exponentially.

Height-height correlation diverges logarithmically.

Results differ from power-law distributions in critical systems.

Abstract

We present numerical data of the height-height correlation function and of the avalanche size distribution for the three dimensional Toom interface. The height-height correlation function behaves samely as the interfacial fluctuation width, which diverges logarithmically with space and time for both unbiased and biased cases. The avalanche size defined by the number of changing sites caused by a single noise process, exhibits an exponentially decaying distribution, which is in contrast to power-law distributions appearing in typical self-organized critical phenomena. We also generalize the Toom model into arbitrary dimensions.