Frustrated nearest-neighbord=2Ising model: Exact results

We study a d=2 Ising model with vertical coupling K>0 and random horizontal coupling KH(KH:K₁{≤}KH,{≤}K₂), 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*=K₂ (Griffith's singularity in temperature); K*=〈K〉, where 〈K〉 is the average horizontal bond (infinite correlation length and {ν}=1), and K*=K₁ (Griffith's singularity, if K₁0, its dual version if not). We show for the last case that F(t){}t1/t.