On the Ising model with strongly anisotropic external field

In this paper we analyze the equilibrium phase diagram of the two-dimension al ferromagnetic n.n. Ising model when the external field takes alternating signs on different rows. We show that some of the zero-temperature coexist ence lints disappear at every positive sufficiently small temperature, wher eas one (and only one) of them persists for sufficiently low temperature.