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Stochastic domination for the Ising and fuzzy Potts models

Marcus Warfheimer (Institutionen för matematiska vetenskaper, matematik)
Electronic Journal of Probability (1083-6489). Vol. 15 (2010), p. 1802-1824.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Stochastic domination, Ising model, fuzzy Potts model, domination of product measures

Denna post skapades 2011-01-21. Senast ändrad 2012-03-19.
CPL Pubid: 135786


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Institutionen för matematiska vetenskaper, matematik (2005-2016)


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