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

Bin-Zhou Mi and Huai-Yu Wang

Physica A: Statistical Mechanics and its Applications, 2025, vol. 674, issue C

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≥3) Heisenberg ferromagnet with an arbitrary spin-S obeys the Td/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.

Keywords: High-dimensional Heisenberg ferromagnet; Low-temperature magnetization; The T\textit {d}/2 law; Lattice structural factor; Curie temperature (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:674:y:2025:i:c:s0378437125003826

DOI: 10.1016/j.physa.2025.130730

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