Crossover in an Exactly Solvable Dimer Model of Domain Walls with Dislocations

An exactly solvable generalized dimer model is proposed. In one limit this model is the isotropic Ising model and in another limit it is the anisotropic Kasteleyn model with radically different critical behavior. The value of the crossover exponent $\phi$ near the multicritical point is determined to be ½. The proposed model is isomorphic to a domain-wall model with dislocations, thereby providing an example of dislocation-mediated crossover in uniaxial commensurate-incommensurate transitions.