QUANTUM RENORMALIZATION OF THE XY MODEL

The statistical mechanics of the two-dimensional ferromagnetic model w ith easy-plane anisotropy is approached by the pure-quantum self-consi stent harmonic approximation (PQSCHA), that reduces the calculation of thermodynamic averages to effective classical expressions. In the PQS CHA, the quantum corrections to the classical thermodynamics are reduc ed to suitable (temperature-dependent) renormalizations of the interac tion parameters, so that the full role of the nonlinear excitations is preserved. A particular case is the XXO model (also known as the quan tum XY model), which undergoes a Kosterlitz-Thouless phase transition at some finite temperature T(c). Since it is possible to calculate how much the effective exchange interaction is weakened by quantum fluctu ations, we can predict, for instance, the corresponding amount of redu ction of T(c) for any value of the spin. Even in the extreme quantum c ase of the spin-1/2 model, our result is compatible with the estimates of T(c) obtained by other authors.