Correlations in inhomogeneous Ising models

Using general methods developed in a previous treatment we study correlations in inhomogeneous Ising models on a square lattice. The nearest neighbour couplings can vary both in strength and sign such that the coupling distribution is translationally invariant in horizontal direction. We calculate correlations parallel to the layering in the horizontally layered model with periodv=2. If the model has a finite critical temperature,T_c>0, the order parameter in the frustrated case may become discontinuous forT0. Correlations atT=T_c decay algebraically with critical exponent =1/4 and exponentially forT>T_c. If the critical temperature vanishes,T_c=0, we always have exponential decay at finite temperatures, while atT=T_c=0 we encounter either long-range order or algebraic decay with critical index =1/2, i.e.T=0 is thus a critical point.Work performed within the research program of the Sonder forschungsbereich 125 Aachen-Jülich-Köln