Defect Lines in the Ising Model and Boundary States on Orbifolds

TL;DR

New features of the Ising defect problem are obtained including a novel universality class of defect lines and the universal boundary to bulk crossover of the spin correlation function.

Abstract

Critical phenomena in the two-dimensional Ising model with a defect line are studied using boundary conformal field theory on the $c=1$ orbifold. Novel features of the boundary states arising from the orbifold structure, including continuously varying boundary critical exponents, are elucidated. New features of the Ising defect problem are obtained including a novel universality class of defect lines and the universal boundary to bulk crossover of the spin correlation function.

Figures (2)

• Figure 1: The folding of the Ising model on a cylinder to a $c=1$ theory on a strip. We fold at the defect line and also at the line on the opposite side. These lines correspond to the boundary in the folded system.
• Figure 2: The two-spin correlation for various strength of the defect. We show the result for (a) $\langle \sigma_1 \sigma_1 \rangle$ and (b) $\langle \sigma_1 \sigma_2 \rangle$ for $\varphi_0 = 0$ (strong coupling and anisotropic limit), $0.1 \pi , 0.2 \pi , 0.25 \pi$ (no defect) , $0.3 \pi , 0.4 \pi$ and $0.5 \pi$ (free boundary condition). They are shown as a function of the (horizontal) distance $r$, in a log-log plot.