Dynamics and thermodynamics of a pair of interacting magnetic dipoles

TL;DR

This paper analytically solves the dynamics of two fixed magnetic dipoles, explores their thermodynamic properties, and validates results with Monte Carlo simulations, advancing understanding of dipole interactions.

Contribution

It provides an exact analytical solution for the equations of motion of two fixed magnetic dipoles and combines this with thermodynamic calculations and numerical validation.

Findings

Analytical solutions for dipole dynamics are derived.

Thermodynamic quantities are calculated across temperature regimes.

Results are validated with Monte Carlo simulations.

Abstract

We consider the dynamics and thermodynamics of a pair of magnetic dipoles interacting via their magnetic fields. We consider only the "spin" degrees of freedom; the dipoles are fixed in space. With this restriction it is possible to provide the general solution of the equations of motion in analytical form. Thermodynamic quantities, such as the specific heat and the zero field susceptibility are calculated by combining low temperature asymptotic series and a complete high temperature expansion. The thermal expectation value of the autocorrelation function is determined for the low temperature regime including terms linear in $T$. Furthermore, we compare our analytical results with numerical calculations based on Monte Carlo simulations.