This article is cited in 16 papers

Dynamical fluctuations at the critical point: convergence to a nonlinear stochastic PDE

L. Bertini^a, E. Presutti^a, B. Rüdiger^a, E. Saada<sup>b

a</sup> Dipartimento di Matematica, Università di Roma Tor Vergata, Roma, Italy
^b Université de Rouen, France

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.

Keywords: Kac potentials, critical fluctuations, stochastic quantization of field theories.

Received: 22.07.1993

Language: English

 English version: Theory of Probability and its Applications, 1993, 38:4, 586–629

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