Néel temperature of a quasi-two-dimensional triangular-lattice antiferromagnet

Based on the atomic representation for spin operators in the case of an arbitrary value of the spin $S$, we study the influence of quantum fluctuations on spin-wave renormalizations of the Néel temperature $T_\mathrm{N}$ and on the magnetization of quasi-two-dimensional triangular-lattice antiferromagnet sublattices. The application of combined Green's functions constructed using spin operators and their partial components allows easily obtaining a closed system of equations determining not only all branches of the spectrum of collective excitations but also the occupation numbers of states of an atom with different values of the spin projection. We show that the renormalization of $T_\mathrm{N}$ is expressed in terms of the generalized Watson integral. Its nontrivial dependence on the degree of quasi-two-dimensionality and on the dynamical properties of three spectral branches determines the behavior of the critical temperature in the cases of different relations between the parameters of the quasi-two-dimensional antiferromagnet.