Phase Transitions in Ehrenfest Urns Model with Interactions: Coexistence of uniform and non-uniform states

TL;DR

This paper generalizes the Ehrenfest urn model to multiple urns with interactions, revealing phase coexistence and transitions, with analytical and simulation validation of the phase diagram and stability properties.

Contribution

It introduces interactions into the Ehrenfest urn model with multiple urns, analytically characterizing phase coexistence and transitions.

Findings

Coexistence of stable uniform and non-uniform phases.

Exact derivation of phase transition thresholds and energy barriers.

Monte Carlo simulations confirm analytical results.

Abstract

A model based on the classic non-interacting Ehrenfest urn model with two-urns is generalized to $M$ urns with the introduction of interactions for particles within the same urn. As the inter-particle interaction strength is varied, phases of different levels of non-uniformity emerge and their stabilities are calculated analytically. In particular, coexistence of locally stable uniform and non-uniform phases connected by first-order transition occurs. The phase transition threshold and energy barrier can be derived exactly together with the phase diagram obtained analytically. These analytic results are further confirmed by Monte Carlo simulations.