Properties of the random field Ising model in a transverse magnetic field

TL;DR

This paper studies how a random longitudinal field affects the quantum phase transition in the Ising model with a transverse magnetic field, revealing a fixed point that governs both quantum and classical transitions and exhibits activated dynamical scaling.

Contribution

It demonstrates that the quantum phase transition is controlled by a fixed point with no quantum fluctuations, linking quantum and classical critical behaviors.

Findings

Long-range order exists at low randomness and transverse field in d>2.

The quantum transition shares critical properties with the classical transition.

Dynamical scaling is activated, with logarithmic divergence of time scales.

Abstract

We consider the effect of a random longitudinal field on the Ising model in a transverse magnetic field. For spatial dimension $d > 2$, there is at low strength of randomness and transverse field, a phase with true long range order which is destroyed at higher values of the randomness or transverse field. The properties of the quantum phase transition at zero temperature are controlled by a fixed point with no quantum fluctuations. This fixed point also controls the classical finite temperature phase transition in this model. Many critical properties of the quantum transition are therefore identical to those of the classical transition. In particular, we argue that the dynamical scaling is activated, i.e, the logarithm of the diverging time scale rises as a power of the diverging length scale.