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

TL;DR

This paper investigates phase transitions in the transverse field Ising model with aperiodic disorder, establishing conditions for phase transitions in ergodic and quasiperiodic cases, especially in one dimension.

Contribution

It provides new criteria for phase transitions in the Ising model with aperiodic disorder, including a sharp condition for quasiperiodic fields in one dimension.

Findings

Phase transition occurs for a $G_\delta$ set of ergodic fields.

A sharp condition for phase transition in 1D quasiperiodic fields.

Identification of a zero temperature phase transition in the model.

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.