On Random Allocation Models in the Thermodynamic Limit
arXiv:2307.14466 · doi:10.1103/PhysRevE.108.064107
Abstract
We discuss the phase transition and critical exponents in the random allocation model (urn model) for different statistical ensembles. We provide a unified presentation of the statistical properties of the model in the thermodynamic limit, uncover new relationships between the thermodynamic potentials and fill some lacunae in previous results on the singularities of these potentials at the critical point and behaviour in the thermodynamic limit. The presentation is intended to be self-contained, so we carefully derive all formulae step by step throughout. Additionally, we comment on a quasi-probabilistic normalisation of configuration weights which has been considered in some recent studies
arXiv commentVarious technical calculations have been moved to appendices, the introduction has been rewritten and some figures have been adjusted for clarity. Accepted for publication in Phys. Rev. E
References in corpus (33)
- Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
- Phase Transitions in one-dimensional nonequilibrium systems
- Condensation in the zero range process: stationary and dynamical properties
- Criterion for phase separation in one-dimensional driven systems
- The Nature of the Condensate in Mass Transport Models
- Canonical Analysis of Condensation in Factorised Steady State
- Condensation in the Backgammon model
- Large deviations for random walks under subexponentiality: the big-jump domain
- Wealth Condensation in Pareto Macro-Economies
- Dynamics of the condensate in zero-range processes
- Zero range model of traffic flow
- A simple stochastic model for the dynamics of condensation
- Phase transition in fluctuating branched geometry
- Phase diagram of the mean field model of simplicial gravity
- Factorised Steady States in Mass Transport Models on an Arbitrary Graph
- Condensation in stochastic particle systems with stationary product measures
- Zero Range Condensation at Criticality
- From urn models to zero-range processes: statics and dynamics
- Modelling one-dimensional driven diffusive systems by the Zero-Range Process
- Condensation for a fixed number of independent random variables
- Finite size effects and metastability in zero-range condensation
- Condensation in zero-range processes on inhomogeneous networks
- Condensation transitions in a model for a directed network with weighted links
- Maximal Diversity and Zipf's Law
- Condensation and extremes for a fluctuating number of independent random variables
- Structure of the condensed phase in the inclusion process
- Longest interval between zeros of the tied-down random walk, the Brownian bridge and related renewal processes
- Collapse of 4D random geometries
- Quantum widening of CDT universe
- Renyi entropy of the totally asymmetric exclusion process
- Comment on `Fluctuation-dominated phase ordering at a mixed order transition'
- Causal and homogeneous networks
- Rényi Entropy of Zeta-Urns