Lattice Gas Models with Long Range Interactions

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.

19 pages, 3 figures

References in corpus (7)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Complete Analysis of Phase Transitions and Ensemble Equivalence for the Curie-Weiss-Potts Model
• The Asymptotics of Large Constrained Graphs
• Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model
• On the phase transition curve in a directed exponential random graph model
• Asymptotic structure and singularities in constrained directed graphs
• Existence of shape-dependent thermodynamic limit in spin systems with short- and long-range interactions