Magnetic defect line in a critical Ising bath

TL;DR

This paper calculates critical exponents for a magnetic defect in the 3D Ising model and explores implications for fermion operators in Fermi surfaces, introducing a generalized cluster algorithm.

Contribution

It provides the first computation of critical exponents for magnetic line defects in the 3D Ising model and generalizes the Wolff algorithm for O(N) systems with magnetic fields.

Findings

Critical exponents for magnetic line defects in 3D Ising model

Anomalous dimension of fermion operator in Fermi surface context

Generalized Wolff cluster algorithm for O(N) spin systems

Abstract

We compute the critical exponents associated with a magnetic line defect in the critical 3D Ising model. From the result, we deduce the anomalous dimension of the fermion operator in the z = 1 scaling regime of a Fermi surface coupled to a O(1) Wilson-Fisher fixed point. We introduce a generalization of the Wolff cluster algorithm to O(N) spin systems with a background magnetic field.