94-373 Maes C. , Vande Velde K.

The fuzzy Potts model (35K, LaTeX) Nov 29, 94

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Abstract. We consider the ferromagnetic $q$-state Potts model on the $d$-dimensional lattice $\integ ^d,\;d\geq 2$. Suppose that the Potts variables $(\rho _x,\; x\in \integ ^d)$ are distributed in one of the $q$ low temperature phases. Suppose that $n\not=1,q$ divides $q$. Partitioning the single site state space into $n$ equal parts $K_1,\ldots ,K_n$, we obtain a new random field $\sigma =(\sigma _x,\; x\in \integ ^d)$ by defining fuzzy variables $\sigma _x=\alpha $ if $\rho _x\in K_{\alpha },\; \alpha =1,\ldots ,n$. We investigate the state induced on these fuzzy variables. First we look at the conditional distribution of $\rho _x$ given all values $\sigma _y, y\in \integ ^d$. We find that below the critical temperature all versions of this conditional distribution are non-quasilocal on a set of configurations which carries positive measure. Then we look at the conditional distribution of $\sigma _x$ given all values $\sigma _y, y\not=x$. If the system is not at the critical temperature of a first order phase transition, there exists a version of this conditional distribution that is almost surely quasilocal.

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