Francesca R. Nardi, Enzo Olivieri, Milos Zahradnik On the Ising model with strongly anisotropic external field (278K, Plaintex) ABSTRACT. In this paper we analyze the equilibrium phase diagram of two-dimensional ferromagnetic n.n. Ising model when the external field takes alternating signs on different rows. We show that some of zero temperature coexistence lines disappear at every positive temperature whereas one (and only one) of them persists for sufficiently low temperature.