Shen, Hao and Weber, Hendrik (2018) Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits. Journal of Functional Analysis, 275 (6). pp. 1321-1367. doi:10.1016/j.jfa.2017.12.014 ISSN 0022-1236.

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Abstract

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 [13] as in [33] but an additional coupling argument is needed to show convergence of the linearized dynamics.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Stochastic partial differential equations, Ising model
Journal or Publication Title:	Journal of Functional Analysis
Publisher:	Academic Press
ISSN:	0022-1236
Official Date:	15 September 2018
Dates:	Date Event 15 September 2018 Published 20 June 2018 Available 4 December 2017 Accepted
Volume:	275
Number:	6
Page Range:	pp. 1321-1367
DOI:	10.1016/j.jfa.2017.12.014
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	8 December 2017
Date of first compliant Open Access:	20 June 2019
RIOXX Funder/Project Grant:	Project/Grant ID RIOXX Funder Name Funder ID DMS-1712684 National Science Foundation http://dx.doi.org/10.13039/100000001

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