Abstract
The most general Pfaffian solution of the staggered ice-rule vertex model on the Kagome lattice is given. It is shown that this 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 for an antiferroelectric model in both staggered and direct fields at a particular temperature is obtained. As the fields vary, the system undergoes transitions among states of zero, partial and complete direct polarization.