Frustrated nearest-neighbord=2Ising model: Exact results

We study a d=2 Ising model with vertical coupling K>0 and random horizontal coupling $K_H$($K_H$:$K_1$≤$K_H$,≤$K_2$), which is the same within a row. This generalizes the McCoy-Wu model since it allows for frustration. By mapping it into a random-field model in d=1, we show that the free energy F has infinitely differentiable singularities at $K^{\mathrm{*}}$=$K_2$ (Griffith’s singularity in temperature); $K^{\mathrm{*}}$=〈K〉, where 〈K〉 is the average horizontal bond (infinite correlation length and ν=1), and $K^{\mathrm{*}}$=$K_1$ (Griffith’s singularity, if $K_1$$t^{1/t}$.