Solid-fluid transition of two- or three-dimensional systems with infinite-range interaction

TL;DR

This paper introduces exactly solvable particle systems with infinite-range interactions to analyze solid-fluid transitions, revealing different order types in various lattice structures, and defining the solid phase via density Fourier components.

Contribution

It presents a novel method to derive the solid--fluid transition from microscopic models with non-decaying potentials, providing exact solutions for these systems.

Findings

First-order transitions in triangular, BCC, FCC lattices.

Second-order transition in simple cubic lattice.

Solid phase characterized by nonzero Fourier density component.

Abstract

It is difficult to derive the solid--fluid transition from microscopic models. We introduce particle systems whose potentials do not decay with distance and calculate their partition function exactly using a method similar to that for lattice systems with infinite-range interaction. In particular, we investigate the behaviors of examples among these models, which become a triangular, body-centered cubic, face-centered cubic, or simple cubic lattice in low-temperature phase. The transitions of the first three examples are of the first order, and that of the last example is of the second order. Note that we define the solid phase as that whose order parameter, or Fourier component of the density, becomes nonzero, and the models we considered obey the ideal-gas law even in the solid phase.