A New Estimate of the Cutoff Value in the Bak-Sneppen Model

2021/11/19 by Fish, C. A., Veerman, J. J. P.
#Computational Physics (physics.comp-ph) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2111.10473

Abstract

We present evidence that the Bak-Sneppen model of evolution on N vertices requires N³ iterates to reach equilibrium. This is substantially more than previous authors suggested (on the order of N²). Based on that estimate, we present a novel algorithm inspired by previous rank-driven analyses of the model allowing for direct simulation of the model with populations of up to N = 25600 for 2⋅ N³ iterations. These extensive simulations suggest a cutoff value of x^* = 0.66692 ± 0.00003, a value slightly lower than previously estimated yet still distinctly above 2/3. We also study how the cutoff values x^*_N at finite N approximate the conjectured value x^* at N=∞. Assuming x^*_N-x^*_∞ ∼ N^-ν, we find that ν=0.978± 0.025, which is significantly lower than previous estimates (ν≈ 1.4).

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