Lattice Gas Models with Long Range Interactions

TL;DR

This paper investigates lattice gas models with long-range interactions, deriving a variational principle for entropy and demonstrating a first-order phase transition in a one-dimensional case.

Contribution

It introduces a rigorous variational framework for entropy in long-range lattice gas models and identifies phase transition behavior.

Findings

Entropy is non-differentiable along a specific curve in the model.

A first-order phase transition is proven in a one-dimensional example.

The study extends understanding of phase behavior in long-range interacting systems.

Abstract

We study microcanonical lattice gas models with long range interactions, including power law interactions. We rigorously obtain a variational principle for the entropy. In a one dimensional example, we find a first order phase transition by proving the entropy is non-differentiable along a certain curve.