Exact Partition Function and Boundary State of Critical Ising Model with Boundary Magnetic Field

TL;DR

This paper calculates the exact partition function and boundary state of the critical 2D Ising model with a boundary magnetic field, revealing the boundary RG flow between free and fixed conditions.

Contribution

It provides an exact computation of the boundary state and ground state degeneracy for the critical Ising model with boundary magnetic field, elucidating boundary RG flows.

Findings

Exact partition function at criticality with boundary magnetic field

Universal ground state degeneracy g computed exactly

Boundary state characterized for the boundary RG flow

Abstract

We compute the exact partition function of the 2D Ising Model at critical temperature but with nonzero magnetic field at the boundary. The model describes a renormalization group flow between the free and fixed conformal boundary conditions in the space of boundary interactions. For this flow the universal ground state degeneracy $g$ and the full boundary state is computed exactly.