The Anisotropic Bak-Sneppen Model

TL;DR

This paper investigates how introducing anisotropy into the Bak-Sneppen model changes its universality class, with analytical and numerical evidence showing different behaviors and a tractable maximally anisotropic case.

Contribution

It demonstrates that anisotropy shifts the Bak-Sneppen model into a different universality class and provides exact solutions for extreme anisotropies.

Findings

Anisotropy causes a crossover in avalanche behavior.

Exact solutions are obtained for zero and maximal anisotropy.

The maximally anisotropic model is more tractable and broadly applicable.

Abstract

The Bak-Sneppen model is shown to fall into a different universality class with the introduction of a preferred direction, mirroring the situation in spin systems. This is first demonstrated by numerical simulations and subsequently confirmed by analysis of the multi-trait version of the model, which admits exact solutions in the extremes of zero and maximal anisotropy. For intermediate anisotropies, we show that the spatiotemporal evolution of the avalanche has a power law ``tail'' which passes through the system for any non-zero anisotropy but remains fixed for the isotropic case, thus explaining the crossover in behaviour. Finally, we identify the maximally anisotropic model which is more tractable and yet more generally applicable than the isotropic system.