Staggered ice-rule vertex model—The Pfaffian solution

Abstract

It is pointed out that the staggered ice-rule model contains a number of outstanding lattice statistical problems including the Ising model in a nonzero magnetic field. The most general Pfaffian solution of this staggered vertex model is studied in this paper. In special cases our solution reduces to that of two recently considered dimer models of phase transitions. It also leads to the exact solution of several vertex models as well as an exact isotherm of a general antiferroelectric model, all in the presence of both direct and staggered fields.