The Analytical Theory of Bulk Melting I: Exact Solution of the One-dimensional Atom Chain

TL;DR

This paper presents an exact analytical solution for a one-dimensional atom chain model to understand the role of interstitialcies in crystal melting, demonstrating the applicability of classical melting criteria in 1D.

Contribution

It provides the first exact solution of a 1D atom chain model incorporating interstitialcies, linking melting behavior to classical criteria.

Findings

Exact partition function and correlation functions derived

Melting point aligns with Lindemann and Born criteria in 1D

Correlation behavior supports classical melting theories

Abstract

We investigate theoretically the crucial r\^{o}le of interstitialcies that trigger the melting of a boundary-free crystal. Based on an interstitialcy model that resembles the $J_1$-$J_2$ model of frustrated antiferromagnets with uniaxial anisotropy, we have calculated the exact partition function and correlation functions in a one-dimensional atom chain. The melting point and correlation behavior of this crystal model show the applicability of Lindemann criterion and Born criterion in the one-dimensional case.