Relevant perturbations at the spin quantum Hall transition

TL;DR

This paper investigates relevant perturbations at the spin quantum Hall transition using a network model and classical percolation mapping, providing exact scaling dimensions and confirming results with simulations.

Contribution

It offers the first exact analytical determination of scaling dimensions of relevant perturbations at this critical point, linking network model perturbations to percolation operators.

Findings

Exact analytical values of scaling dimensions obtained.

Multiple network perturbations correspond to the same percolation operator.

Numerical simulations confirm analytical predictions.

Abstract

We study relevant perturbations at the spin quantum Hall critical point using a network model formulation. The model has been previously mapped to classical percolation on a square lattice, and we use the mapping to extract exact analytical values of the scaling dimensions of the relevant perturbations. We find that several perturbations that are distinct in the network model formulation correspond to the same operator in the percolation picture. We confirm our analytical results by comparing them with numerical simulations of the network model.