Thermodynamics of Ising models with layered randomness: Exact solutions on square and triangular lattices

Abstract
Two-dimensional Ising models are studied on square and triangular lattices with layered disordered bonds (McCoy-Wu-type models). It is shown that exact solutions exist for diluted exponential distributions of couplings. In the ferromagnetic case the free energy exhibits an essential singularity (slightly different from the result of McCoy and Wu) at the transition point. If frustration is present the transitions occurs at T=0, and the specific heat is linear.