Differential equation for local magnetization in the boundary Ising model

TL;DR

This paper derives a second order linear differential equation involving Painleve III functions that describes the local magnetization in the boundary Ising model with a boundary magnetic field.

Contribution

It establishes a novel differential equation framework for local magnetization in the boundary Ising model using Painleve functions.

Findings

Derived differential equation for local magnetization

Connected magnetization to Painleve III functions

Provides analytical tools for boundary Ising models

Abstract

We show that the local magnetization in the massive boundary Ising model on the half-plane with boundary magnetic field satisfies second order linear differential equation whose coefficients are expressed through Painleve function of the III kind.