Staggered ice-rule vertex model (on a square lattice)

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Abstract
The authors have studied the staggered ice-rule vertex model on a square lattice which allows different vertex weights for the four sublattices of the square lattice. The most general Pfaffian solution is given. It is shown that the model may exhibit up to three phase transitions. The specific heat diverges with an exponent 1/2 either above or below each transition temperature. The exact isotherm of an antiferroelectric model in the presence of both direct and staggered fields at a particular temperature is obtained. As the fields are varied, the system undergoes transitions among states of zero, partial and complete direct polarization.

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