Generalization of exactly-solvable model to exhibit solid-fluid phase transition in crystal structures with two particles in a primitive cell

TL;DR

This paper extends an exactly-solvable infinite-range cosine potential model to more complex lattice structures with two particles per primitive cell, enabling exact analysis of solid-fluid phase transitions in these systems.

Contribution

It generalizes previous models to include complex lattice structures with multiple particles per primitive cell, broadening the scope of exact solvability.

Findings

Exact partition function derivation for complex lattices

Demonstration of solid-fluid phase transition in new lattice types

Framework applicable to a wider class of crystal structures

Abstract

In our previous paper [H. K., J.Stat.Mech.(2015) P08020], we investigated an interacting-particle model with infinite-range cosine potentials, and derived the partition function which shows solid-fluid phase transition by exact calculation. However, we could treat only simple lattice structures in which more than one stable point exist in a primitive cell such as the triangular or face-centered cubic lattice. In the present paper, we generalize our previous scheme to more complicated lattice structures with two particles in a primitive cell. Generalization to more complicated lattice structures is straightforward.