Free Energy of the Classical Heisenberg Model

Abstract

High-temperature power-series expansions for the free energy of a classical Heisenberg ferromagnet in an applied field are given in the form $\frac{\ensuremath{-}F}{\mathrm{NkT}}=\ensuremath{\Sigma}\stackrel{}{n,l}{a}_{2n,l}{h}^{2n}{x}^{l},$ where $h=\frac{g\ensuremath{\beta}H}{kT}$ and $x=\frac{J}{kT}$. The coefficients are given for $l\ensuremath{\le}7$ and $4\ensuremath{\le}2n\ensuremath{\le}10$. Estimates of the critical exponents for the fourth to tenth field derivatives of $F$ are given.