Quantum-classical correspondence for spins at finite temperatures: theory and applications

A. El Mendili; M. E. Zhitomirsky

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arXiv · 2602.16501

Quantum-classical correspondence for spins at finite temperatures: theory and applications

A. El Mendili·M. E. Zhitomirsky

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Abstract

We derive a rigorous quantum-to-classical mapping for interacting spin systems at finite temperatures. Specifically, the large-$S$ asymptotic form of the partition function is given by the partition function of a classical model for vectors of length $S_C=\sqrt{S(S+1)}$. Quantum corrections to the asymptotic result form a series in powers of $1/[S(S+1)]$. We calculate the leading temperature-independent quantum correction to the magnetic anisotropy constant. The established mapping justifies the use of classical Monte Carlo simulations for realistic magnetic Hamiltonians, including anisotropic and frustrated interactions. As an application, we compute the Curie and N\'eel temperatures for a range of magnetic materials with known microscopic interaction constants. The obtained transition temperatures are in good agreement with measured values. Monte Carlo results for the magnetic susceptibility of the collinear antiferromagnet MnF$_2$ above and below the transition are also compared with experimental data.

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A. El Mendili, M. E. Zhitomirsky. 2026-02-18. Quantum-classical correspondence for spins at finite temperatures: theory and applications. https://arxiv.org/abs/2602.16501

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