In this paper we analyze the equilibrium phase diagram of the two-dimensional ferromagnetic n.n. Ising model when the external field takes alternating signs on different rows. We show that some of the zero-temperature coexistence lines disappear at every positive sufficiently small temperature, whereas one (and only one) of them persists for sufficiently low temperature.
Nardi, F. R., Olivieri, E., & Zahradnik, M. (1999). On the Ising model with strongly anisotropic external field. Journal of Statistical Physics, 97(1-2), 87-144. https://doi.org/10.1023/A:1004662917583