Numerical renormalization group study of random transverse Ising models in one and two space dimensions

TL;DR

This paper uses a numerical renormalization group approach to study the quantum critical behavior and Griffiths-McCoy singularities of random transverse Ising models in one and two dimensions, confirming universality classes and estimating critical exponents.

Contribution

It introduces a numerical implementation of the Ma-Dasgupta-Hu renormalization group scheme for higher dimensions and applies it to 1D and 2D random quantum Ising models.

Findings

Critical exponents in the double chain match those of the simple chain.

Estimated exponents in 2D are consistent with recent studies.

The method confirms the universality class across different geometries.

Abstract

The quantum critical behavior and the Griffiths-McCoy singularities of random quantum Ising ferromagnets are studied by applying a numerical implementation of the Ma-Dasgupta-Hu renormalization group scheme. We check the procedure for the analytically tractable one-dimensional case and apply our code to the quasi-one-dimensional double chain. For the latter we obtain identical critical exponents as for the simple chain implying the same universality class. Then we apply the method to the two-dimensional case for which we get estimates for the exponents that are compatible with a recent study in the same spirit.