Real-space renormalization-group approach to the random transverse-field Ising model in finite dimensions

TL;DR

This paper develops a real-space renormalization-group method to analyze the critical behavior of the random transverse-field Ising model in finite dimensions, providing new insights into phase diagrams and fixed points.

Contribution

It introduces a scheme that accurately determines critical points and exponents, extending analysis to spin glasses in transverse fields in 2D and 3D.

Findings

Exact critical point and exponent in 1D

Reproduction of known results in 2D and 3D

Evidence for infinite-randomness fixed point in spin glasses

Abstract

The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent nu in one dimension and some previous results in the case of random ferromagnetic interactions are reproduced in two and three dimensions. We apply the scheme to spin glasses in transverse fields in two and three dimensions, which have not been analyzed very extensively. The phase diagrams and the critical exponent nu are obtained and evidence for the existence of an infinite-randomness fixed point in these models is found.