Abstract
We consider an Ising spin system with Glauber dynamics and Kac interactions in one dimension at the critical temperature. We study the fluctuation filed of the magnetization density in a scaling limit which involves space, time and the range of the interaction. We prove that for a suitable choice of the scalings the normalized fluctuations field converges to the solution of a one-dimensional (nonlinear) Ginzburg–Landau equation perturbed by a white noise process.
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