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Stochastic Domination for the Ising and Fuzzy Potts Models

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1.	Title	Title of document	Stochastic Domination for the Ising and Fuzzy Potts Models
2.	Creator	Author's name, affiliation, country	Marcus Warfheimer; Chalmers University of Technology and University of Gothenburg; Sweden
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)	Stochastic domination; Ising model; fuzzy Potts model; domination of product measures
3.	Subject	Subject classification	60K35
4.	Description	Abstract	We discuss various aspects concerning stochastic domination for the Ising model and the fuzzy Potts model. We begin by considering the Ising model on the homogeneous tree of degree $d$, $\mathbb{T}^d$. For given interaction parameters $J_1$, $J_2>0$ and external field $h_1\in\mathbb{R}$, we compute the smallest external field $\tilde{h}$ such that the plus measure with parameters $J_2$ and $h$ dominates the plus measure with parameters $J_1$ and $h_1$ for all $h\geq\tilde{h}$. Moreover, we discuss continuity of $\tilde{h}$ with respect to the three parameters $J_1$, $J_2$, $h_1$ and also how the plus measures are stochastically ordered in the interaction parameter for a fixed external field. Next, we consider the fuzzy Potts model and prove that on $\mathbb{Z}^d$ the fuzzy Potts measures dominate the same set of product measures while on $\mathbb{T}^d$, for certain parameter values, the free and minus fuzzy Potts measures dominate different product measures
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2010-11-14
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ejp.ejpecp.org/article/view/820
10.	Identifier	Digital Object Identifier	10.1214/EJP.v15-820
11.	Source	Journal/conference title; vol., no. (year)	Electronic Journal of Probability; Vol 15
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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