Boundary conformal field theory approach to the two-dimensional critical Ising model with a defect line

TL;DR

This paper analyzes the critical 2D Ising model with a defect line using boundary conformal field theory, revealing a new universality class and providing exact correlation functions and free energy terms.

Contribution

It introduces a boundary conformal field theory approach to classify and analyze defect lines in the 2D Ising model, identifying a new universality class.

Findings

Complete spectrum of boundary operators derived

Exact two-point correlation functions obtained

Universal free energy term for defect lines calculated

Abstract

We study the critical two-dimensional Ising model with a defect line (altered bond strength along a line) in the continuum limit. By folding the system at the defect line, the problem is mapped to a special case of the critical Ashkin-Teller model, the continuum limit of which is the $Z_2$ orbifold of the free boson, with a boundary. Possible boundary states on the $Z_2$ orbifold theory are explored, and a special case is applied to the Ising defect problem. We find the complete spectrum of boundary operators, exact two-point correlation functions and the universal term in the free energy of the defect line for arbitrary strength of the defect. We also find a new universality class of defect lines. It is conjectured that we have found all the possible universality classes of defect lines in the Ising model. Relative stabilities among the defect universality classes are discussed.