Exact Partition Function and Boundary State of 2-D Massive Ising Field Theory with Boundary Magnetic Field

TL;DR

This paper derives exact expressions for the partition function, boundary state, and ground state degeneracy of the 2-D massive Ising model with boundary magnetic field, revealing boundary bound states and RG flow behavior.

Contribution

It provides the first exact formulas for the partition function and boundary states of the off-critical 2-D Ising model with boundary magnetic field.

Findings

Exact partition function and boundary state expressions derived.

Identification of boundary bound states and their properties.

Recovery of boundary RG flow in the massless limit.

Abstract

We compute the exact partition function, the universal ground state degeneracy and boundary state of the 2-D Ising model with boundary magnetic field at off-critical temperatures. The model has a domain that exhibits states localized near the boundaries. We study this domain of boundary bound state and derive exact expressions for the ``$g$ function'' and boundary state for all temperatures and boundary magnetic fields. In the massless limit we recover the boundary renormalization group flow between the conformally invariant free and fixed boundary conditions.