Uniqueness and exponential decay of correlations for some two-dimensional spin lattice systems

We consider a two-dimensional lattice spin system which naturally arises in dynamical systems called coupled map lattice. The configuration space of the spin system is a direct product of mixing subshifts of finite type. The potential is defined on the set of all squares in Z(2) and decays exponentially with the linear size of the square. Via the polymer expansion technique we prove that for sufficiently high temperatures the limit Gibbs distribution is unique and has an exponential decay of correlations.