THE FUZZY POTTS-MODEL

We consider the ferromagnetic q-state Ports model on the d-dimensional lattice Z(d), d greater than or equal to 2. Suppose that the Ports va riables (rho(x), x is an element of Z(d)) are distributed in one of th e q low-temperature phases. Suppose that n not equal 1, q divides q. P artitioning the single-site state space into n equal parts K-l,..., K- n, we obtain a new random field sigma = (sigma(x), x is an element of Z(d)) by defining fuzzy variables sigma(x) = alpha if rho(x) is an ele ment of K-alpha, alpha = 1,...,n. We investigate the state induced on these fuzzy variables. First we look at the conditional distribution o f rho(x) given all values sigma(gamma), gamma is an element of Z(d). W e find that below the coexistence point all versions of this condition al distribution are non-quasilocal on a set of configurations which ca rries positive measure. Then we look at the conditional distribution o f sigma(x) given all values sigma(gamma), gamma not equal x. If the sy stem is not at the coexistence point of a first-order phase transition , there exists a version of this conditional distribution that is almo st surely quasilocal.