Bistability in an Ising model with non-Hamiltonian dynamics

We investigate the phenomenon of magnetization bistability in a two-dimensional Ising model with a non-Hamiltonian Glauber dynamics by means of Monte Carlo simulations. This effect has previously been observed in the Toom model, which supports two stable phases with different magnetizations, even in the presence of a nonzero field. We find that such bistability is also present in an Ising model in which the transition probabilities are expressed in terms of Boltzmann factors depending only on the nearest-neighbor spins and the associated bond strengths. The strength on each bond assumes different values with respect to the spins at either of its ends, introducing an asymmetry like that of the Toom model.