Infinite disorder scaling of random quantum magnets in three and higher dimensions

TL;DR

This paper investigates the critical behavior of random quantum magnets in three and higher dimensions using an advanced numerical method, revealing universal infinite disorder quantum critical points and smooth variation of critical exponents with dimension.

Contribution

The study extends the strong disorder renormalization group analysis to higher dimensions and complex graphs, confirming the universality and infinite disorder nature of quantum critical points.

Findings

Identification of infinite disorder quantum critical points in 3D and 4D

Critical exponents are independent of disorder form

Critical exponents vary smoothly with dimensionality

Abstract

Using a very efficient numerical algorithm of the strong disorder renormalization group method we have extended the investigations about the critical behavior of the random transverse-field Ising model in three and four dimensions, as well as for Erd\H os-R\'enyi random graphs, which represent infinite dimensional lattices. In all studied cases an infinite disorder quantum critical point is identified, which ensures that the applied method is asymptotically correct and the calculated critical exponents tend to the exact values for large scales. We have found that the critical exponents are independent of the form of (ferromagnetic) disorder and they vary smoothly with the dimensionality.