THE LYAPUNOV EXPONENT FOR MAGNONS IN BINARY SPIN-GLASS CHAINS

We present a calculation of the Lyapunov exponent for transverse magnon modes in a Heisenberg spin-glass chain with positive and negative exchange interactions, both analytically as a microcanonical average and also numerically in the usual canonical statistical ensemble. In the positive-omega regime we find that the localization length obeys xi(omega) is-proportional-to omega-1 at omega --> 0 if p > q, where p, q = 1 - p are the +1 and -1 spin concentrations, respectively. It is shown that the previously reported xi(omega) is-proportional-to omega-2/3 singularity, related to the anomalous dispersion law omega is-proportional-to k3/2, holds only in the limit of equal concentrations p = q = 0.5. The corresponding densities of states diverge as rho(omega) is-proportional-to omega-1/2 and is-proportional-to omega-1/3 for p > q and p = q, respectively.