Boundary critical phenomena of the random transverse Ising model in D>=2 dimensions

TL;DR

This study investigates the boundary critical phenomena of the random transverse Ising model in dimensions 2, 3, and 4 using strong disorder renormalization group methods, revealing dimension-dependent surface exponents and scaling behaviors.

Contribution

It provides the first numerical analysis of boundary critical behavior in the random transverse Ising model across multiple dimensions using strong disorder renormalization group techniques.

Findings

Surface magnetization exponents increase with dimension: 1.60, 2.65, 3.7.

Surface exponents are independent of disorder form.

Critical magnetization profiles exhibit specific scaling in various geometries.

Abstract

Using the strong disorder renormalization group method we study numerically the critical behavior of the random transverse Ising model at a free surface, at a corner and at an edge in D=2, 3 and 4-dimensional lattices. The surface magnetization exponents are found to be: x_s=1.60(2), 2.65(15) and 3.7(1) in D=2, 3 and 4, respectively, which do not depend on the form of disorder. We have also studied critical magnetization profiles in slab, pyramid and wedge geometries with fixed-free boundary conditions and analyzed their scaling behavior.