Thermodynamics of the classical spin triangle

TL;DR

This paper analyzes the thermodynamics of a classical three-spin system with Heisenberg interaction, providing explicit calculations of key quantities and comparing them with simulations, revealing unique long-time autocorrelation behaviors.

Contribution

It offers explicit semi-analytical calculations of thermodynamic properties for the classical spin triangle, including novel insights into long-time autocorrelation decay.

Findings

Agreement between analytical calculations and Monte Carlo simulations

Identification of $1/t$ damped oscillations in autocorrelation functions

Proposal of a theoretical explanation for long-time decay behavior

Abstract

The classical spin system consisting of three spins with Heisenberg interaction is an example of a completely integrable mechanical system. In this paper we explicitly calculate thermodynamic quantities as density of states, specific heat, susceptibility and spin autocorrelation functions. These calculations are performed (semi-)analytically and shown to agree with corresponding Monte Carlo simulations. For the long-time autocorrelation function, we find, for certain values of the coupling constants, a decay to constant values in the form of an $1/t$ damped harmonic oscillation and propose a theoretical explanation.