The versions of the self-consistent spin-wave theories (SSWT) of two-dimensional Heisenberg ferro- and antiferromagnets with a weak interlayer coupling and/or magnetic anisotropy, that are based on the nonlinear Dyson-Maleev, Schwinger, and combined boson-pseudofermion representations, are analyzed. Analytical results for the temperature dependences of (sublattice) magnetization and the short-range order parameter, and the critical points are obtained. The influence of external magnetic field is considered. Fluctuation corrections to SSWT are calculated within a random-phase approximation which takes into account correctly leading and next-leading logarithmic singularities. These corrections are demonstrated to improve radically the agreement with experimental data on layered perovskites and other systems. Thus an account of these fluctuations provides a quantitative theory of layered magnets.
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Irkhin et al. (1999) studied this question.
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