Quantum-classical correspondence for spins at finite temperatures with application to Monte Carlo simulations

TL;DR

This paper establishes a rigorous quantum-to-classical mapping for interacting spin systems at finite temperatures, enabling accurate classical Monte Carlo simulations of magnetic materials.

Contribution

It provides a theoretical framework for classical modeling of quantum spin systems, including quantum corrections, and applies it to compute transition temperatures of real magnetic materials.

Findings

Asymptotic partition function matches classical model in large-S limit.

Quantum corrections form a series in powers of 1/[S(S+1)].

Monte Carlo transition temperatures agree with experimental data.

Abstract

We consider quantum-to-classical mapping for an arbitrary system of interacting spins at finite temperatures. We prove that, in the large-$S$ limit, the asymptotic form of the partition function coincides with that of a classical model for spins of length $S_C=\sqrt{S(S+1)}$. Quantum corrections to the leading term form a series in powers of $1/[S(S+1)]$. This representation provides a rigorous basis for classical modeling of realistic magnetic Hamiltonians. As an application, the classical Monte Carlo simulations are performed to compute transition temperatures for several topical materials with known interaction parameters, including MnF$_2$, MnTe, Rb$_2$MnF$_4$, MnPSe$_3$, FePS$_3$, FePSe$_3$, CoPS$_3$, CrSBr, and CrI$_3$. The resulting transition temperatures show good agreement with experimental data.