Modified Thirring model beyond the excluded-volume approximation

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.

26 pages, 8 figures

References in corpus (8)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Random changes of flow topology in two dimensional and geophysical turbulence
• Hamiltonian dynamics reveals the existence of quasi-stationary states for long-range systems in contact with a reservoir
• Incomplete equilibrium in long-range interacting systems
• Long-range interacting systems in the unconstrained ensemble
• Dynamical large deviations for homogeneous systems with long range interactions and the Balescu--Guernsey--Lenard equation
• Microcanonical characterization of first-order phase transitions in a generalized model for aggregation
• Monte Carlo simulations in the unconstrained ensemble