Exact solution of a Z(4) gauge Potts model on planar lattices

The exact solution of a general Z(4) gauge Potts model with a single and do uble plaquette representation of the action is found on a subspace of gauge -coupling parameters on the square and triangular lattices. The two Ising-t ype critical lines of a second-order phase transition for the model on a sq uare lattice are found. For the model on a triangular lattice the two criti cal surfaces of an Ising-type and two nontrivial lines of a second-order ph ase transition with different critical behavior than an the critical surfac es are found. It is shown that a two-dimensional (2D) general Z(4) gauge Po tts model with single and double plaquette representation of the action and a 2D spin-3/2 Ising model belong to the same universality class. [S1063-65 1X(99)03910-0].