On Ising Correlation Functions with Boundary Magnetic Field

TL;DR

This paper derives differential equations and explicit formulas for one-point and two-point functions of the Ising model with a boundary magnetic field, advancing understanding of boundary effects in statistical physics.

Contribution

It provides new exact differential equations and explicit formulas for correlation functions in the Ising model with boundary magnetic field, including the massless limit.

Findings

Derived differential equations for one-point functions.

Obtained explicit formulas for massless limit correlation functions.

Enhanced understanding of boundary effects in the Ising model.

Abstract

Exact expressions of the boundary state and the form factors of the Ising model are used to derive differential equations for the one-point functions of the energy and magnetization operators of the model in the presence of a boundary magnetic field. We also obtain explicit formulas for the massless limit of the one-point and two-point functions of the energy operator.