Nonequilibrium phase diagram of Ising model with competing dynamics

We analyze the stationary nonequilibrium state of a spin system evolving under combined flips at temperature ${\mathrm{\beta }}^{\mathrm{-}1}$ and exchanges at β=0. Computer simulations indicate that the phase transition changes, as the exchange rate Γ increases, from second to first order. We interpret this as a changeover from Ising behavior for small Γ to mean-field behavior for Γ→∞ where the magnetization is discontinuous in the ‘‘continuum limit.’’