Monte Carlo Calculation of the Scaling Equation of State for the Classical Heisenberg Ferromagnet

Using a Monte Carlo procedure with a self-consistent-field boundary condition, the magnetization of a simple cubic classical Heisenberg ferromagnet with nearest-neighbor interactions only is calculated. For reduced temperatures and reduced fields in the range $0.02<~|\frac{T}{T_c}-1|$, $\frac{H}{J}<~0.5$ the data of this computer experiment can be described in terms of the "effective" critical exponents $0.31<~\beta <~0.35$, $1.33<~\gamma <~1.39$, and $4.9<~\delta <~5.3$. Although the present data are not very close to the critical point they do obey the homogeneity requirement and determine the scaling function rather precisely. This function agrees very well with the scaling function for the face-centered-cubic classical Heisenberg magnet derived recently by Milošević and Stanley using high-temperature—series-expansion techniques. This agreement supports their hypothesis that neither critical exponents nor the scaling function depend on the lattice structure in the Heisenberg model.