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Stochastic domination for the Ising and fuzzy Potts models

Marcus Warfheimer (Institutionen för matematiska vetenskaper, matematik)
(2010)
[Preprint]

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 $d$, $\Td$. For given interaction parameters $J_1$, $J_2>0$ and external field $h_1\in\RR$, 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 $J_1$, $J_2$, $h$ 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 $\Zd$ the fuzzy Potts measures dominate the same set of product measures while on $\Td$, for certain parameter values, the free and minus fuzzy Potts measures dominate different product measures. For the Ising model, Liggett and Steif proved that on $\Zd$ the plus measures dominate the same set of product measures while on $\T^2$ that statement fails completely except when there is a unique phase.



Denna post skapades 2010-03-19. Senast ändrad 2010-04-20.
CPL Pubid: 118145

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Annan matematik

Chalmers infrastruktur

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Denna publikation ingår i:


Interacting particle systems in varying environment, stochastic domination in statistical mechanics and optimal pairs trading in finance


Ingår i serie

Preprint - Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University 2010:21