Replica Symmetry Breaking in the Random Replicant Model
P Biscari & G Parisi
TL;DR
This paper investigates a statistical mechanics model of coevolving species with random interactions, revealing replica symmetry breaking at high competition levels and providing analytical solutions compared with numerical simulations.
Contribution
It introduces a one-step replica symmetry breaking solution for the model and compares it with numerical results, advancing understanding of complex species interactions.
Findings
Replica symmetry is broken at high competition.
Analytical solutions match numerical simulations.
Provides insights into species coevolution dynamics.
Abstract
We study the statistical mechanics of a model describing the coevolution of species interacting in a random way. We find that at high competition replica symmetry is broken. We solve the model in the approximation of one step replica symmetry breaking and we compare our findings with accurate numerical simulations.
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