TIME-DEPENDENT CRITICAL FLUCTUATIONS OF A ONE-DIMENSIONAL LOCAL MEAN-FIELD MODEL

One-dimensional stochastic Ising systems with a local mean field interaction (Kac potential) are investigated, It is shown that near the critical temperature of the equilibrium (Gibbs) distribution the time dependent process admits a scaling limit given by a nonlinear stochastic PDE. The initial conditions of this approximation theorem are then verified for equilibrium states when the temperature goes to its critical value in a suitable way, Earlier results of Bertini-Presutti-Rudiger-Saada are improved, the proof is based on an energy inequality obtained by coupling the Glauber dynamics to its voter type, linear approximation.