6 research outputs found
Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits
We study the Glauber dynamics of a two dimensional Blume-Capel model (or
dilute Ising model) with Kac potential parametrized by - the
"inverse temperature" and the "chemical potential". We prove that the locally
averaged spin field rescales to the solution of the dynamical equation
near a curve in the plane and to the solution of the dynamical
equation near one point on this curve. Our proof relies on a discrete
implementation of Da Prato-Debussche method as in a result by Mourrat-Weber but
an additional coupling argument is needed to show convergence of the linearized
dynamics.Comment: 42 pages, 1 figur