Frustrated nearest-neighbor d=2 Ising 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 (Griffiths singularity in temperature); K*=K, where K is the average horizontal bond (infinite correlation length and =1), and K*=K1 (Griffiths singularity, if K1<0, its dual version if not). We show for the last case that F(t)t1/t.