Abstract
Thermodynamics of quantum and classical two-dimensional (2D) Heisenberg models with long-range dipole--dipole interaction has been investigated using various forms of self-consistent spin-wave theory (SSWT). It has been found that SSWT gives a much lower transition temperature ${T}_{c}$ than the free-magnon (spin-wave) theory. For the classical spin, the ${T}_{c}$ from SSWT lies within 9% of the Monte Carlo value, making SSWT the best approximation among those considered. It is proven that the random phase approximation vertex corrections to SSWT are rather small. The results depend strongly on the value of the spin, emphasizing the importance of using the quantum and not the classical 2D Heisenberg model even for large spins such as $S=7∕2$.
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