The energy density of an Ising half plane lattice

TL;DR

This paper calculates the energy density of a half-plane Ising lattice with boundary magnetic field at various temperatures, comparing exact results with recent complex analysis methods at critical temperature.

Contribution

It provides an exact expression for the energy density of the half-plane Ising model with boundary magnetic field at arbitrary temperatures, linking it to recent analytical approaches.

Findings

Exact energy density expression at arbitrary temperature.

Comparison with recent critical temperature calculations.

Insights into boundary effects on Ising lattice energy density.

Abstract

We compute the energy density at arbitrary temperature of the half plane Ising lattice with a boundary magnetic field $H_b$ at a distance $M$ rows from the boundary and compare limiting cases of the exact expression with recent calculations at $T=T_c$ done by means of discrete complex analysis methods.