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 [13] as in [33] but an additional coupling argument is needed to show convergence of the linearized dynamics.
Original language | English |
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Pages (from-to) | 1321-1367 |
Journal | Journal of Functional Analysis |
Volume | 275 |
Issue number | 6 |
Early online date | 20 Jun 2018 |
DOIs | |
Publication status | Published - 15 Sept 2018 |
Funding
We would like to thank Weijun Xu for many helpful discussions on phase coexistence models and the dynamical Φ 4 equations. H.S. was partially supported by the NSF through DMS-1712684 . Appendix A
Keywords
- Blume–Capel
- Glauber dynamics
- Stochastic PDE
ASJC Scopus subject areas
- Analysis