  We study a unitary version of the one-dimensional Anderson model, given by a
five diagonal deterministic unitary operator multiplicatively perturbed by a
random phase matrix. We fully characterize positivity and vanishing of the
Lyapunov exponent for this model throughout the spectrum and for arbitrary
distributions of the random phases. This includes Bernoulli distributions,
where in certain cases a finite number of critical spectral values, with
vanishing Lyapunov exponent, exists. We establish similar results for a unitary
version of the random dimer model.
