Random Ising chain in transverse and longitudinal fields: Strong disorder RG study

TL;DR

This paper investigates the low-energy behavior of a disordered Ising chain with both transverse and longitudinal random fields using strong disorder RG, revealing phase transitions and fixed points relevant to quantum and classical disordered systems.

Contribution

It extends the strong disorder RG analysis to include simultaneous random transverse and longitudinal fields, identifying new disordered fixed points and phase behavior.

Findings

In absence of longitudinal fields, the system has quantum-ordered and disordered phases separated by an infinite disorder critical point.

Introducing a random longitudinal field destroys the ordered phase, leading to two distinct disordered fixed points.

A separatrix exists between the two disordered phases, originating from the infinite disorder fixed point, with strong quantum fluctuations.

Abstract

Motivated by the compound ${\rm LiHo}_x{\rm Y}_{1-x}{\rm F}_4$, we consider the Ising chain with random couplings and in the presence of simultaneous random transverse and longitudinal fields, and study its low-energy properties at zero temperature by the strong disorder renormalization group approach. In the absence of longitudinal fields, the system exhibits a quantum-ordered and a quantum-disordered phase separated by a critical point of infinite disorder. When the longitudinal random field is switched on, the ordered phase vanishes and the trajectories of the renormalization group are attracted to two disordered fixed points: one is characteristic of the classical random field Ising chain, the other describes the quantum disordered phase. The two disordered phases are separated by a separatrix that starts at the infinite disorder fixed point and near which there are strong quantum fluctuations.