Levy-Nearest-Neighbors Bak-Sneppen Model

TL;DR

This paper investigates a generalized Bak-Sneppen model with power-law distributed neighbor selection, revealing how critical exponents depend on the decay parameter and suggesting a critical dimension of six.

Contribution

It introduces a variable neighbor selection mechanism in the Bak-Sneppen model and analyzes how critical properties depend on the decay exponent, challenging previous assumptions about the model's critical dimension.

Findings

Exponents depend on the power-law decay parameter ta.

Results align with high-dimensional Bak-Sneppen simulations.

Proposes a critical dimension d_c=6, differing from earlier claims.

Abstract

We study a random neighbor version of the Bak-Sneppen model, where "nearest neighbors" are chosen according to a probability distribution decaying as a power-law of the distance from the active site, P(x) \sim |x-x_{ac }|^{-\omega}. All the exponents characterizing the self-organized critical state of this model depend on the exponent \omega. As \omega tends to 1 we recover the usual random nearest neighbor version of the model. The pattern of results obtained for a range of values of \omega is also compatible with the results of simulations of the original BS model in high dimensions. Moreover, our results suggest a critical dimension d_c=6 for the Bak-Sneppen model, in contrast with previous claims.