Spin excitations in an anisotropic $J_1$–$J_2$ Heisenberg model

We investigate the spin-wave excitation spectrum in an antiferromagnet for the anisotropic $J_1$–$J_2$ and isotropic quasi-two-dimensional Heisenberg models with an arbitrary spin $S$. We consider the random phase approximation (Tyablikov decoupling) and the linear spin-wave approximation. We calculate the temperature dependence of the magnetization and the Néel temperature and compare it with experimental results for high-temperature cuprate superconductors and iron-based compounds.