Peculiarities of thermodynamics of $2D$ Heisenberg magnets on a triangular lattice

Thermodynamic and magnetic properties of $2D$ Heisenberg ferro- and antiferromagnets with a spin of $1/2$ on a triangular lattice are investigated theoretically. The formalism of two-time Green’s functions and the decoupling procedure explicitly taking into account the presence of a short-range order and not requiring the existence of a long-range order in the system are used. The energy, heat capacity, and susceptibility of magnets are expressed in terms of correlation functions for which a self-consistent system of equations is obtained. The system is solved numerically in the entire temperature range. Analytic asymptotic forms of the above quantities are constructed in the limits of high and low temperatures. The results of analysis are compared with analogous data for square lattices as well as with the high-temperature expansions available in literature.