Local Magnetization in Critical Ising Model with Boundary Magnetic Field

TL;DR

This paper presents a straightforward method to derive spin correlation functions in the 2D critical Ising model with boundary magnetic field, explicitly calculating local magnetization for specific geometries.

Contribution

It introduces a simple approach to compute boundary magnetization in the 2D critical Ising model with boundary magnetic field, providing explicit formulas for half-plane and disk geometries.

Findings

Explicit formulas for local magnetization in half-plane and disk geometries.

A new method simplifies the derivation of boundary spin correlation functions.

Enhanced understanding of boundary effects in the 2D critical Ising model.

Abstract

We discribe a simple way to derive spin correlation functions in 2D Ising model at critical temperature but with nonzero magnetic field at the boundary. Local magnetization (i.e. one-point function) is computed explicitly for half-plane and disk geometries.