Statistical Mechanics of a Two-Dimensional System with Long Range Interaction

TL;DR

This paper investigates the statistical mechanics of a 2D lattice gas with long-range interactions, revealing a transition from a liquid to a glassy state with aging phenomena through analytic and Monte Carlo methods.

Contribution

It introduces a simplified geometric approach to analyze long-range interactions in a 2D lattice gas, combining analytic calculations with Monte Carlo simulations.

Findings

Identification of a dynamical transition between liquid and glassy states

Observation of aging behavior in two-time correlation functions

Simplification of the mathematical analysis due to geometric structure

Abstract

We analyse the statistical physics of a two dimensional lattice based gas with long range interactions. The particles interact in a way analogous to Queens on a chess board. The long range nature of the interaction gives the mathematics of the problem a simple geometric structure which simplifies both the analytic and numerical study of the system. We present some analytic calculations for the statics of the problem and also we perform Monte Carlo simulations which exhibit a dynamical transition between a high temperature liquid regime and a low temperature glassy regime exhibiting aging in the two time correlation functions.