Thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet with long-range interactions via the spectral density method

TL;DR

This paper investigates the thermodynamic behavior of a classical long-range interacting spin-S Heisenberg ferromagnet across different dimensions and decay exponents, using the spectral density method.

Contribution

It applies the spectral density method to analyze the thermodynamics of long-range interacting classical Heisenberg ferromagnets, confirming conditions for long-range order and determining critical temperatures.

Findings

Long-range order exists at finite temperature for specific ranges of p and d.

Critical temperatures are explicitly calculated.

The study confirms known theorems about long-range order in such systems.

Abstract

The thermodynamic properties of a classical d-dimensional spin-S Heisenberg ferromagnet, with long-range interactions decaying as $r^{-p}$ and in the presence of an external magnetic field, is investigated by means of the spectral density method in the framework of classical statistical mechanics. We find that long-range order exists at finite temperature for $d<p<2d$ with $d\leq 2$ and for $p>d$ with $d>2$, consistently with known theorems. Besides, the related critical temperature is determined and a study of the critical properties is performed.