On the spontaneous magnetization of the classical Heisenberg ferromagnet

Abstract

An equation of the form 0= Sigma n=0infinity xn beta n(m/x) where x=J/kT, m=M/Ng beta is derived for the magnetization of the classical Heisenberg ferromagnet in zero external field. The functions beta 0 to beta 9 inclusive are given. This equation is used to plot the reduced magnetization m as a function of temperature just below Tc. A value of 0.38 is obtained for the critical exponent beta in the temperature range 0.92<xcx<0.99 (with xc=0.1573). The magnetization at very low temperatures is also mentioned.