@article{EJP820,
author = {Marcus Warfheimer},
title = {Stochastic Domination for the Ising and Fuzzy Potts Models},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {15},
year = {2010},
keywords = {Stochastic domination; Ising model; fuzzy Potts model; domination of product measures},
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},
pages = {no. 58, 1802-1824},
issn = {1083-6489},
doi = {10.1214/EJP.v15-820},
url = {http://ejp.ejpecp.org/article/view/820}}