An exactly solvable phase transition model: generalized statistics and generalized Bose-Einstein condensation

TL;DR

This paper introduces an exactly solvable statistical model for a generalized Bose-Einstein condensation phase transition, providing rigorous mathematical criteria for phase transition detection and characterization.

Contribution

It develops a novel exactly solvable model based on generalized statistics with variable maximum occupation numbers, extending traditional Bose-Einstein and Fermi-Dirac frameworks.

Findings

Exact thermodynamic expressions for gas and condensed phases

Mathematically rigorous criteria for phase transition detection

Introduction of generalized statistics with variable occupation limits

Abstract

In this paper, we present an exactly solvable phase transition model in which the phase transition is purely statistically derived. The phase transition in this model is a generalized Bose-Einstein condensation. The exact expression of the thermodynamic quantity which can simultaneously describe both gas phase and condensed phase is solved with the help of the homogeneous Riemann-Hilbert problem, so one can judge whether there exists a phase transition and determine the phase transition point mathematically rigorously. A generalized statistics in which the maximum occupation numbers of different quantum states can take on different values is introduced, as a generalization of Bose-Einstein and Fermi-Dirac statistics.