Replica Symmetry Breaking in the Random Replicant Model

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.

12 pages, TeX, 5 postscript figures are avalaible upon request, submitted to Journal of Physics A: Mathematical and General

Cited by in corpus (20)

• Marginally Stable Equilibria in Critical Ecosystems
• Properties of equilibria and glassy phases of the random Lotka-Volterra model with demographic noise
• Dynamically evolved community size and stability of random Lotka-Volterra ecosystems
• Generalized Lotka-Volterra equations with random, non-reciprocal interactions: the typical number of equilibria
• Species Abundance Patterns in Complex Evolutionary Dynamics
• Random replicators with asymmetric couplings
• Random replicators with high-order interactions
• Rank abundance relations in evolutionary dynamics of random replicators
• Ecological communities from random generalised Lotka-Volterra dynamics with non-linear feedback
• Well-mixed Lotka-Volterra model with random strongly competitive interactions
• Effects of intraspecific cooperative interactions in large ecosystems
• Quenched complexity of equilibria for asymmetric Generalized Lotka-Volterra equations
• Extinctions in the random replicator model
• Two-population replicator dynamics and number of Nash equilibria in random matrix games
• Dynamics of random replicators with Hebbian interactions
• Bose-Einstein-Like condensation of deformed random matrix: A replica approach
• Microbiomes Through The Looking Glass: Linking species interactions to dysbiosis through a disordered Lotka-Volterra framework
• Instance Space of the Number Partitioning Problem
• Gradient dynamics in reinforcement learning
• Interaction-free ergodicity-breaking driven by temporally hyperuniform noise