Finite-temperature phase transitions across spin symmetries in two-dimensional magnets

Abstract

Recent advances in intrinsic two-dimensional (2D) magnets have created a need for a unified understanding of finite-temperature phase transitions across different spin-symmetry classes. Here, we investigate finite-temperature magnetism in the classical 2D Heisenberg model using large-scale Monte Carlo simulations, continuously spanning the easy-plane, isotropic, and easy-axis regimes. We find that characteristic temperatures are strongly affected by the interplay of finite-size effects and spin symmetry, induced by magnetocrystalline anisotropy, being most pronounced in the isotropic Heisenberg regime and substantially reduced toward the easy-plane and easy-axis limits. Examining Berezinskii--Kosterlitz--Thouless (BKT) physics in the easy-plane regime, we find that the characteristic temperatures independently estimated from the magnetization and heat capacity deviate significantly from those proposed by BKT theory, but match a previously reported anomaly in the XY-model. We report that characteristic temperatures instead are correlated with the proliferation of vortex-antivortex pairs, suggesting the gain in entropy by their accelerated nucleation as the origin of the anomaly. Establishing this connection both theoretically and numerically, we argue that the thermodynamic characteristic temperature in finite easy-plane Heisenberg magnets, including the deviation from BKT theory, is subject to the interplay between finite-size spin correlations and vortex proliferation. These results clarify how experimental and technologically relevant temperature scales evolve with magnetic anisotropy, spin symmetry, and system size in finite 2D magnets.