  We study a class of stationary processes indexed by $\Z^d$ that are defined
via minors of $d$-dimensional (multilevel) Toeplitz matrices. We obtain
necessary and sufficient conditions for phase multiplicity (the existence of a
phase transition) analogous to that which occurs in statistical mechanics.
Phase uniqueness is equivalent to the presence of a strong $K$ property, a
particular strengthening of the usual $K$ (Kolmogorov) property. We show that
all of these processes are Bernoulli shifts (isomorphic to i.i.d. processes in
the sense of ergodic theory). We obtain estimates of their entropies and we
relate these processes via stochastic domination to product measures.
