Ising model with a boundary magnetic field - an example of a boundary flow

TL;DR

This paper demonstrates the application of a nonperturbative proof of the g-theorem to the 2D Ising model with a boundary magnetic field, providing explicit calculations and insights into boundary flow phenomena.

Contribution

It offers a detailed example of the g-theorem proof in a boundary perturbed 2D Ising model, including explicit computations of relevant quantities.

Findings

Explicit calculation of boundary flow in the Ising model

Verification of the g-theorem in a boundary magnetic field context

Analysis of contact terms in boundary perturbations

Abstract

In hep-th/0312197 a nonperturbative proof of the g-theorem of Affleck and Ludwig was put forward. In this paper we illustrate how the proof of hep-th/0312197 works on the example of the 2D Ising model at criticality perturbed by a boundary magnetic field. For this model we present explicit computations of all the quantities entering the proof including various contact terms. A free massless boson with a boundary mass term is considered as a warm-up example.