ZETA-FUNCTION FOR THE LYAPUNOV EXPONENT OF A PRODUCT OF RANDOM MATRICES

A cycle expansion for the Lyapunov exponent of a product of random mat rices is derived. The formula is nonperturbative and numerically effec tive, which allows the Lyapunov exponent to be computed to high accura cy. In particular, the free energy and the heat capacity are computed for the one-dimensional Ising model with quenched disorder. The formul a is derived by using a Bernoulli dynamical system to mimic the random ness.