SPIN-WAVE THEORY OF THE SPIN 1/2 XY MODEL

The spin wave theory of Kondo and Yamaji is applied to the spin 1/2 XY model in one to three dimensions. In one dimension, the value of the gap⊿ which appears in the spectrum of x-component spin remains finite up to 0 K, and no phase transition occurs. The value of the nearest neighbour correlation function is in good agreement with the exact values. In three dimensions, ⊿ vanishes at a finite temperature, and the second order phase transition occurs. In two dimensions, as T⟶0, ⊿ becomes very small for square lattice and tends to zero as exp (—T0/T) for triangular lattice, which means the non-existence of the phase transition. The susceptibility, however, becomes anomalously large for low temperatures, and the extrapolation of Curie-Weiss law gives a “fictitious” transition temperature whose value agrees with those given by the high temperature expansion and the real space renormalization group theory. © 1979, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.