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Title: The dynamical Ising-Kac model converges to 桅^4 in three dimensions.

Abstract. The Glauber dynamics of the Ising-Kac model describes the evolution of spins on a lattice, with the flipping rate of each spin depending on an average field in a large neighborhood. Giacomin, Lebowitz, and Presutti conjectured in the 90s that the random fluctuations of the process near the critical temperature coincide with the solution of the dynamical 桅^4 model. This conjecture was proved in one dimension by Bertini, Presutti, Ruediger, and Saada in 1993 and the two-dimensional case was proved by Mourrat and Weber in 2014. Our result settles the conjecture in the three-dimensional case.

The dynamical 桅^4 model is given by a non-linear stochastic partial differential equation which is driven by an additive space-time white noise and which requires renormalization of the non-linearity in dimensions two and three. The renormalization has a physical meaning and corresponds to a small shift of the inverse temperature of the discrete system away from its critical value.

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