A d=2 dimensional kinetic Ising model that evolves by a combination of spin flips and spin exchanges is investigated. The spin flips satisfy detailed balance for the equilibrium state of the Ising model at temperature T while the spin exchanges are random Lévy flights of dimension σ=1.5. Our Monte Carlo (MC) simulations show that the steady state of this system displays a second-order phase transition as T is lowered. Comparing the critical fluctuations of the magnetization to those of an Ising model in which the interaction decays with distance as ${\mathit{r}}^{\mathrm{-}3.5}$, we find that, within the resolution of the MC data, the critical exponents and the scaling functions of the two systems coincide. We argue that this coincidence indicates that a recent conjecture about the random Lévy flights generating long-range interaction of the form ${\mathit{V}}_{\mathrm{eff}}$(r)∼${\mathit{r}}^{\mathrm{-}\mathit{d}\mathrm{-}\mathrm{\sigma }}$ is valid not only in the spherical limit and in d=1 but also in d=2.

• Received 17 June 1992

DOI:https://doi.org/10.1103/PhysRevE.47.1520