Glauber dynamics of 2 D Kac - Blume - Capel model and their stochastic PDE limits
نویسندگان
چکیده
Abstract We study the Glauber dynamics of a two dimensional Blume-Capel model (or dilute Ising model) with Kac potential parametrized by (β, θ) the “inverse temperature” and the “chemical potential”. We prove that the locally averaged spin field rescales to the solution of the dynamical Φ4 equation near a curve in the (β, θ) plane and to the solution of the dynamical Φ6 equation near one point on this curve. Our proof relies on a discrete implementation of Da Prato-Debussche method [DPD03] as in [MW16] but an additional coupling argument is needed to show convergence of the linearized dynamics.
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