LONG-RANGE INTERACTIONS GENERATED BY RANDOM LEVY FLIGHTS - SPIN-FLIP AND SPIN-EXCHANGE KINETIC ISING-MODEL IN 2 DIMENSIONS

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 temp erature T while the spin exchanges are random Levy flights of dimensio n sigma=1.5. Our Monte Carlo (MC) simulations show that the steady sta te of this system displays a second-order phase transition as T is low ered. Comparing the critical fluctuations of the magnetization to thos e of an Ising model in which the interaction decays with distance as r -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 a rgue that this coincidence indicates that a recent conjecture about th e random Levy flights generating long-range interaction of the form V( eff)(r) is similar to r(-d-sigma) is valid not only in the spherical l imit and in d=1 but also in d=2.