Microcanonical Monte Carlo Study of One Dimensional Self-Gravitating Lattice Gas Models

TL;DR

This paper uses Microcanonical Monte Carlo simulations to explore one-dimensional self-gravitating lattice gas models, examining the effects of particle size, system geometry, and packing fraction on thermodynamic behaviors like negative heat capacity.

Contribution

It introduces a novel $1/r$ model with linear symmetry and compares the effects of hard-core potentials and geometry on gravitational system properties.

Findings

Low packing fractions preserve negative heat capacity.

High packing fractions cause models to resemble known mean field and 1D systems.

Hard-core particles influence system density and thermodynamic behavior.

Abstract

In this study we present a Microcanonical Monte Carlo investigation of one dimensional self-gravitating toy models. We study the effect of hard-core potentials and compare to those results obtained with softening parameters and also the effect of the geometry of the models. In order to study the effect of the geometry and the borders in the system we introduce a model with the symmetry of motion in a line instead of a circle, which we denominate as $1/r$ model. The hard-core particle potential introduces the effect of the size of particles and, consequently, the effect of the density of the system that is redefined in terms of the packing fraction of the system. The latter plays a role similar to the softening parameter $\epsilon$ in the softened particles' case. In the case of low packing fractions both models with hard-core particles show a behavior that keeps the intrinsic properties of the three dimensional gravitational systems such as negative heat capacity. For higher values of the packing fraction the ring the system behaves as the Hamiltonian Mean Field model and while for the $1/r$ it is similar to the one-dimensional systems.