STABILITY OF ISING SYSTEMS AGAINST NON-HAMILTONIAN, SYMMETRY-BREAKING DYNAMICS

We investigate two two-dimensional Ising models with a non-Hamiltonian Glauber dynamics. The transition probabilities are expressed in terms of Boltzmann factors depending only on the nearest neighbour spins and the associated bond strengths. However, the bond strength on each lattice edge is two-valued; it assumes different values with respect to the spins at either of its ends. In one of the two models, the bond strength pattern is consistent with the four-fold rotational symmetry of the square lattice. In contrast, a preferred direction is present in the second model. This model can be interpreted in terms of inhomogeneous interactions and temperature such that their ratios, i.e. the couplings, are uniform. Monte Carlo simulations of these models show that the phase transition persists when these two types of non-Hamiltonian dynamics are introduced. Furthermore, our results indicate that both models belong to the Ising universality class.