Critical exponents of the anisotropic Bak-Sneppen model

TL;DR

This paper investigates the critical behavior of the anisotropic Bak-Sneppen model, deriving new exact relations and exponents, and confirming findings through simulations and numerical analysis.

Contribution

It extends the understanding of the Bak-Sneppen model by deriving a new exact equation for avalanche sizes and confirming the critical exponent relations in the anisotropic case.

Findings

Established a relation between critical exponents tau and mu for the anisotropic model.

Derived an exact equation for avalanche spatial size distribution in one dimension.

Confirmed critical exponents through Monte Carlo simulations and numerical integration.

Abstract

We analyze the behavior of spatially anisotropic Bak-Sneppen model. We demonstrate that a nontrivial relation between critical exponents tau and mu=d/D, recently derived for the isotropic Bak-Sneppen model, holds for its anisotropic version as well. For one-dimensional anisotropic Bak-Sneppen model we derive a novel exact equation for the distribution of avalanche spatial sizes, and extract the value gamma=2 for one of the critical exponents of the model. Other critical exponents are then determined from previously known exponent relations. Our results are in excellent agreement with Monte Carlo simulations of the model as well as with direct numerical integration of the new equation.