The Ising model in a random magnetic field h is studied on a square lattice. h has the same value along a row, but varies randomly from row to row. h=±∞ with probability p/2 and is zero with probability 1-p. The quenched free energy F and specific heat C are calculated exactly. We find C∼lnp for small p at the Onsager temperature $T_c$. It is shown that for p≠0, F(p,T) is not analytic in T at T=$T_c$, i.e., it has a Griffiths-like singularity.

• Received 13 September 1984

DOI:https://doi.org/10.1103/PhysRevB.31.6089