The characterization of ground states

TL;DR

This paper studies the behavior of equilibrium distributions of infinite particle systems as temperature approaches zero, extending known results from lattice systems to continuous spaces with interaction restrictions.

Contribution

It generalizes the characterization of ground states from lattice particles to particles in R^n under certain interaction constraints.

Findings

Support of limiting distributions characterized at zero temperature

Extension from lattice to continuous space systems

Conditions on interactions for the results

Abstract

We consider limits of equilibrium distributions as temperature approaches zero, for systems of infinitely many particles, and characterize the support of the limiting distributions. Such results are known for particles with positions on a fixed lattice; we extend these results to systems of particles on R^n, with restrictions on the interaction.