For
a generalized Su–Schrieffer–Heeger model, the energy zero is always
critical and hyperbolic in the sense that all reduced transfer matrices
commute and have their spectrum off the unit circle. Disorder-driven
topological phase transitions in this model are characterized by a
vanishing Lyapunov exponent at the critical energy. It is shown that
away from such a transition the density of states vanishes at zero
energy with an explicitly computable Hölder exponent, while it has a
characteristic divergence (Dyson spike) at the transition points. The
proof is based on renewal theory for the Prüfer phase dynamics and the
optional stopping theorem for martingales of suitably constructed
comparison processes.