Condensation in the Backgammon model

TL;DR

This paper investigates a simple balls-in-boxes model that exhibits a phase transition akin to phenomena in random geometry models and generalizes the backgammon model to explore glassy behavior without disorder.

Contribution

It introduces a generalized balls-in-boxes model that captures phase transition phenomena similar to those in complex geometric models and extends the backgammon model's framework.

Findings

The model exhibits a fluid to condensed phase transition.

It demonstrates behavior analogous to random geometries in multiple dimensions.

The model generalizes the backgammon model to include glassy dynamics without disorder.

Abstract

We analyse the properties of a very simple ``balls-in-boxes'' model which can exhibit a phase transition between a fluid and a condensed phase, similar to behaviour encountered in models of random geometries in one, two and four dimensions. This model can be viewed as a generalisation of the backgammon model introduced by Ritort as an example of glassy behaviour without disorder.