Dynamical fluctuations at the critical point: convergence to a~nonlinear stochastic PDE
Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 689-741
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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.
@article{TVP_1993_38_4_a0,
author = {L. Bertini and E. Presutti and B. R\"udiger and E. Saada},
title = {Dynamical fluctuations at the critical point: convergence to a~nonlinear stochastic {PDE}},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {689--741},
publisher = {mathdoc},
volume = {38},
number = {4},
year = {1993},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a0/}
}
TY - JOUR AU - L. Bertini AU - E. Presutti AU - B. Rüdiger AU - E. Saada TI - Dynamical fluctuations at the critical point: convergence to a~nonlinear stochastic PDE JO - Teoriâ veroâtnostej i ee primeneniâ PY - 1993 SP - 689 EP - 741 VL - 38 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a0/ LA - en ID - TVP_1993_38_4_a0 ER -
%0 Journal Article %A L. Bertini %A E. Presutti %A B. Rüdiger %A E. Saada %T Dynamical fluctuations at the critical point: convergence to a~nonlinear stochastic PDE %J Teoriâ veroâtnostej i ee primeneniâ %D 1993 %P 689-741 %V 38 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a0/ %G en %F TVP_1993_38_4_a0
L. Bertini; E. Presutti; B. Rüdiger; E. Saada. Dynamical fluctuations at the critical point: convergence to a~nonlinear stochastic PDE. Teoriâ veroâtnostej i ee primeneniâ, Tome 38 (1993) no. 4, pp. 689-741. http://geodesic.mathdoc.fr/item/TVP_1993_38_4_a0/