Localization for the Ising model in a transverse field with generic aperiodic disorder

Abstract

We show that the transverse field Ising model undergoes a zero temperature phase transition for a $G_{\delta }$ set of ergodic transverse fields. We apply our results to the special case of quasiperiodic transverse fields, in one dimension we find a sharp condition for the existence of a phase transition.

39 pages