  Statistical mechanics of two coupled vector fields is studied in the
tight-binding model that describes propagation of polarized light in discrete
waveguides in the presence of the four-wave mixing. The energy and power
conservation laws enable the formulation of the equilibrium properties of the
polarization state in terms of the Gibbs measure with positive temperature. The
transition line $T=\infty$ is established beyond which the discrete vector
solitons are created. Also in the limit of the large nonlinearity an analytical
expression for the distribution of Stokes parameters is obtained which is found
to be dependent only on the statistical properties of the initial polarization
state and not on the strength of nonlinearity. The evolution of the system to
the final equilibrium state is shown to pass through the intermediate stage
when the energy exchange between the waveveguides is still negligible. The
distribution of the Stokes parameters in this regime has a complex multimodal
structure strongly dependent on the nonlinear coupling coefficients and the
initial conditions.

Statistical Mechanics;Chaotic Dynamics;Optics