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Bulletin of the American Physical Society

Simulations of Magnetic Noise in Classical XY and Heisenberg Spin Models

D. L. Mickelsen, Hervé M. Carruzzo, Ruqian Wu, Clare C. Yu

Published Mar 16, 2021• 0 citations
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We analyse the low-temperature behaviour of the classical isotropic ferromagnetic Heisenberg model on a two-dimensional square lattice of finite size. Presence of a residual magnetization in a finite-size system enables us to use a low-temperature approximation, which is however more restricting than the usual spin-wave approximation known to give reliable results for the XY model at low temperatures T . For the system considered, we find that the spin–spin correlation function decays as 1/ r η( T ) for large separations r bringing about the presence of a quasi-long-range ordering. We give analytic estimates for the exponent η( T ) in different regimes and support our findings by Monte Carlo simulations of the model on lattices of different sizes at different temperatures.