Symmetry-breaking phase transition in a dynamical decision model

TL;DR

This paper models how agents choose between two shops based on product freshness, revealing phase transitions between symmetric and asymmetric customer distributions through simulations and analytical methods.

Contribution

It introduces a decision model incorporating freshness-based satisfaction, demonstrating symmetry-breaking phase transitions with both continuous and discontinuous characteristics.

Findings

Identifies a phase transition from symmetric to asymmetric shop popularity.

Shows both continuous and discontinuous transitions depending on parameters.

Uses numerical simulations and mean-field analysis for validation.

Abstract

We consider a simple decision model in which a set of agents randomly choose one of two competing shops selling the same perishable products (typically food). The satisfaction of agents with respect to a given store is related to the freshness of the previously bought products. Agents select with a higher probability the store they are most satisfied with. Studying the model from a statistical physics perspective, both through numerical simulations and mean-field analytical methods, we find a rich behaviour with continuous and discontinuous phase transitions between a symmetric phase where both stores maintain the same level of activity, and a phase with broken symmetry where one of the two shops attracts more customers than the other.