Thermodynamic properties of high-dimensional Heisenberg ferromagnets with an arbitrary spin-S

Abstract

This study extends the Heisenberg ferromagnetic model to high-dimensional simple hypercubic lattice systems by using the double-time Green’s function method. Analytical derivation and numerical calculation were performed on the lattice structural factor, Curie temperature, and spontaneous magnetization. It is found that the spontaneous magnetization of $d$-dimensional ($d\ge 3$) Heisenberg ferromagnet with an arbitrary spin-$S$ obeys the T^d/2 law at very low temperatures. This indicates that the low-temperature magnetization characteristics are closely related to the spatial dimension. The lattice structural factor is evaluated for $d=3$ to 15. It is interesting to note that when the spatial dimension $d$ is very large, the Curie temperature is nearly proportional to the $d$ at any fixed spin-$S$, which means that the Curie temperature increases with the $d$ with no upper limit. In addition, it is observed that the larger the spin-$S$, the closer the normalized spontaneous magnetization versus the normalized temperature curves for different spatial dimension $d$.