Stochastic domination for the Ising and fuzzy Potts models
Artikel i vetenskaplig tidskrift, 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

Författare

Marcus M J Warfheimer

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Electronic Journal of Probability

1083-6489 (ISSN)

Vol. 15 1802-1824

Ämneskategorier

Sannolikhetsteori och statistik

DOI

10.1214/EJP.v15-820