Momentum coupling of classical atoms

TL;DR

This paper introduces the dual-space cluster expansion method to analyze phase transitions in classical systems by examining cluster formations and their densities, revealing thresholds for infinite cluster emergence.

Contribution

It proposes a novel dual-space cluster expansion technique that links particle momenta to phase transition analysis in classical continuum systems.

Findings

Finite clusters have a density threshold for forming infinite clusters in higher dimensions.

The phase transition involves a singularity in the free energy.

Infinite clusters are always present in condensed phases, varying in size.

Abstract

A new method, dual-space cluster expansion, is proposed to study classical phases transitions in the continuum. It relies on replacing the particle positions as integration variables by the momenta of the relative displacements of particle pairs. Due to the requirement that the particles must be static, coupling via the momenta partitions the set of particles into a set of clusters, and transforms the partition function into a sum over the different cluster decompositions. This allows us to derive a formula for the density that finite clusters can carry in the infinite system. In a simplified example, we then demonstrate that in two and higher dimensions this density has a threshold, beyond which the particles form infinite clusters. The transition is accompanied by a singularity in the free energy. We also show that infinite clusters are always present in condensed phases, most likely submacroscopic in liquids and macroscopic in crystals.