Journal of Physics A. Mathematical and General vol:28 issue:15 pages:4261-4270
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 variables (rho(x), x is an element of Z(d)) are distributed in one of the q low-temperature phases. Suppose that n not equal 1, q divides q. Partitioning 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 element of K-alpha, alpha = 1,...,n. We investigate the state induced on these fuzzy variables. First we look at the conditional distribution of rho(x) given all values sigma(gamma), gamma is an element of Z(d). We find that below the coexistence point 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(gamma), gamma not equal x. If the system is not at the coexistence point of a first-order phase transition, there exists a version of this conditional distribution that is almost surely quasilocal.