On the boundary Ising model with disorder operators

TL;DR

This paper extends bosonisation methods to boundary Ising models with disorder operators, enabling calculation of boundary correlation functions and expectation values, and connecting to known partition functions.

Contribution

It adapts boundary state techniques to include disorder operators in the boundary Ising model, facilitating correlation function computations.

Findings

Calculated boundary disorder operator expectation values on a cylinder.

Reproduced standard and frustrated partition functions in specific limits.

Derived correlation functions on the upper half plane.

Abstract

We extend the well-known method of calculating bulk correlation functions of the conformal Ising model via bosonisation to situations with boundaries. Oshikawa and Affleck have found the boundary states of two decoupled Ising models in terms of the orbifold of a single free boson compactified on a circle of radius r=1; we adapt their results to include disorder operators. Using these boundary states we calculate the expectation value of a single disorder field on a cylinder with free boundary conditions and show that in the appropriate limits we recover the standard and frustrated partition functions. We also show how to calculate Ising correlation functions on the upper half plane.