Random quantum Ising chains with competing interactions

TL;DR

This paper investigates the critical behavior of a quantum Ising chain with competing random interactions, analyzing how the inclusion of long-range couplings affects the stability of the infinite disorder transition.

Contribution

It extends the study of quantum Ising chains to small world networks, revealing the instability of the infinite disorder transition with added long-range couplings.

Findings

The chain's critical point renormalizes to the Fisher fixed point.

Long-range couplings destabilize the infinite disorder transition.

The model's topology scaling is crucial for understanding phase transitions.

Abstract

In this paper we discuss the criticality of a quantum Ising spin chain with competing random ferromagnetic and antiferromagnetic couplings. Quantum fluctuations are introduced via random local transverse fields. First we consider the chain with couplings between first and second neighbors only and then generalize the study to a quantum analog of the Viana-Bray model, defined on a small world random lattice. We use the Dasgupta-Ma decimation technique, both analytically and numerically, and focus on the scaling of the lattice topology, whose determination is necessary to define any infinite disorder transition beyond the chain. In the first case, at the transition the model renormalizes towards the chain, with the infinite disorder fixed point described by Fisher. This corresponds to the irrelevance of the competition induced by the second neighbors couplings. As opposed to this case, this infinite disorder transition is found to be unstable towards the introduction of an arbitrary small density of long range couplings in the small world models.