Nonadditivity in Quasiequilibrium States of Spin Systems with Lattice Distortion

TL;DR

This paper investigates an elastic spin model demonstrating nonadditivity and ensemble inequivalence, revealing long-range effective interactions and the natural applicability of Kac's prescription in such systems.

Contribution

It introduces a short-range elastic spin model that exhibits nonadditivity, ensemble inequivalence, and long-range effective interactions, with numerical evidence supporting these phenomena.

Findings

Negative specific heat or susceptibility depending on ensemble

Effective spin interactions are long-ranged

Kac's prescription naturally applies to the effective interaction

Abstract

It is pointed out that there exists a short-range interacting system, i.e. the elastic spin model, which is extensive but nonadditive. It is numerically shown that, depending on the statistical ensemble, the specific heat or the susceptibility becomes negative in a certain parameter region, which shows ensemble inequivalence in this model. Further, we numerically estimate the effective Hamiltonian for spin variables, and it is clarified that the effective interaction among spin variables is long-ranged. Remarkably, the so called Kac's prescription, which is usually regarded as a mathematical operation to make the system extensive, naturally holds in the effective interaction.