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arXiv · 1708.00948

Convergence of Glauber dynamic on Ising-like models with Kac interaction to $\Phi^{2n}_2$

Massimo Iberti
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Abstract

It has been recently shown by H.Weber and J.C. Mourrat, for the two-dimensional Ising-Kac model at critical temperature, that the fluctuation field of the magnetization, under the Glauber dynamic, converges in distribution to the solution of a non linear ill-posed SPDE: the dynamical $\Phi^4_2$ equation. In this article we consider the case of the multivatiate stochastic quantization equation $\Phi^{2n}_2$ on the two-dimensional torus, and we answer to a conjecture of H.Weber and H.Shen. We show that it is possible to find a state space for a spin system on the two-dimensional discrete torus undergoing Glauber dynamic with ferromagnetic Kac potential, such that the fluctuation field converges in distribution to $\Phi^{2n}_2$.

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Massimo Iberti. 2017-08-02. Convergence of Glauber dynamic on Ising-like models with Kac interaction to $\Phi^{2n}_2$. https://arxiv.org/abs/1708.00948

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