On the High-dimensional Bak-Sneppen model

TL;DR

This paper presents extensive simulations of the Bak-Sneppen model in high dimensions, revealing complex behaviors such as fractal avalanche clusters, transience, and the approach to mean field exponents at the upper critical dimension.

Contribution

It identifies the upper critical dimension of the Bak-Sneppen model as d=8 and describes the transition from complex to mean field behavior with increasing dimensionality.

Findings

Avalanche clusters become fractal for d>2.

The process becomes transient for d≥4.

Exponents reach mean field values at d=8.

Abstract

We report on extensive numerical simulations on the Bak-Sneppen model in high dimensions. We uncover a very rich behavior as a function of dimensionality. For d>2 the avalanche cluster becomes fractal and for d \ge 4 the process becomes transient. Finally the exponents reach their mean field values for d=d_c=8, which is then the upper critical dimension of the Bak Sneppen model.