Stochastic domination for the Ising and fuzzy Potts models
Journal article, 2010

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, T-d. For given interaction parameters J(1), J(2) > 0 and external field h(1) is an element of R, we compute the smallest external field (h) over tilde 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 >= (h) over tilde. Moreover, we discuss continuity of (h) over tilde 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 Z(d) the fuzzy Potts measures dominate the same set of product measures while on T-d, for certain parameter values, the free and minus fuzzy Potts measures dominate different product measures.

fuzzy Potts model

Stochastic domination

domination of product measures

Ising model

Author

Marcus M J Warfheimer

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Electronic Journal of Probability

1083-6489 (ISSN)

Vol. 15 1802-1824

Subject Categories

Probability Theory and Statistics

DOI

10.1214/EJP.v15-820

More information

Created

10/6/2017