Long-range order for a kinetic Ising model at infinite temperature

The two-dimensional Ising model in contact with a heat bath at infinite temperature, T → ∞, is considered. The model is subject to two competing stochastic processes: the Glauber dynamics with probability p and the Kawasaki one with probability (1 − p). The Glauber process is associated to the random flipping of single spins at T → ∞, while the spin exchange Kawasaki dynamics occurs at T → 0−, what increases the energy of the system. We show that the model exhibits a continuous transition from the paramagnetic to the antiferromagnetic phase at the critical value pc = 0.073±0.003. We have used Monte Carlo simulations and finite size analysis in order to calculate the critical probability and the critical exponents of the model. Surprisingly, our value found for the critical probability is almost the same as the critical noise parameter of the isotropic majority-vote model on a square lattice.