Real-space renormalization group for the transverse-field Ising model in two and three dimensions

TL;DR

This paper applies a generalized real-space renormalization group method to analyze the critical behavior of the two- and three-dimensional transverse-field Ising models, achieving accurate estimates of critical exponents.

Contribution

It extends a renormalization group approach from one dimension to higher dimensions, providing the first accurate estimates of critical exponents in (2+1) and (3+1) dimensions.

Findings

Critical exponent ν estimates agree with classical Ising models in higher dimensions.

Method yields exact critical points and exponents in the analyzed models.

First successful application of real-space RG in (2+1) and (3+1) dimensions.

Abstract

The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent $\nu$. The resulting values of the critical exponent $\nu$ in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. This is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.