Approximate Mapping of Two-Dimensional Quantum-Spin Models on Staggered Eight-Vertex Models

Analytic results have been obtained for the thermodynamics of the two-dimensional $S=\frac{1}{2}$ $X-Y$ model using the simplest form of the generalized Trotter formula for the partition function. The model exhibits a phase transition of unconventional nature. It is claimed that this is one of the best descriptions given so far of the critical thermodynamics of the $S=\frac{1}{2}$ two-dimensional $X-Y$ model. Central in the present approach is the mapping of a family of two-dimensional $S=\frac{1}{2}$ models on staggered eight-vertex models having unconventional weights.