Modified Thirring model beyond the excluded-volume approximation

TL;DR

This paper investigates a modified Thirring model with long-range interactions, analyzing equilibrium states under open conditions using simulations and theory, revealing potential first-order phase transitions beyond traditional approximations.

Contribution

It introduces a generalized theoretical framework for long-range systems beyond the excluded-volume approximation and compares open and fixed-particle ensembles.

Findings

First-order phase transitions can occur in the unconstrained ensemble.

Theoretical predictions are confirmed by Monte Carlo simulations.

The model extends understanding of long-range interactions beyond traditional approximations.

Abstract

Long-range interacting systems may exhibit ensemble inequivalence and can possibly attain equilibrium states under completely open conditions, for which energy, volume and number of particles simultaneously fluctuate. Here we consider a modified version of the Thirring model for self-gravitating systems with attractive and repulsive long-range interactions in which particles are treated as hard spheres in dimension d=1,2,3. Equilibrium states of the model are studied under completely open conditions, in the unconstrained ensemble, by means of both Monte Carlo simulations and analytical methods and are compared with the corresponding states at fixed number of particles, in the isothermal-isobaric ensemble. Our theoretical description is performed for an arbitrary local equation of state, which allows us to examine the system beyond the excluded-volume approximation. The simulations confirm the theoretical prediction of the possible occurrence of first-order phase transitions in the unconstrained ensemble. This work contributes to the understanding of long-range interacting systems exchanging heat, work and matter with the environment.