Explicit matrix representation for the Hamiltonian of the one dimensional \mbox{spin~$1/2$} Ising model in mutually orthogonal external magnetic fields

TL;DR

This paper derives an explicit matrix representation for the Hamiltonian of a one-dimensional spin-1/2 Ising model in orthogonal magnetic fields and uses it to analytically compute the ground state energy to fourth order.

Contribution

It introduces a new explicit matrix form of the Hamiltonian for the model, enabling analytical calculations of ground state energy in perpendicular fields.

Findings

Explicit matrix representation of the Hamiltonian derived.

Analytical expression for ground state energy obtained.

Results applicable to understanding spin interactions in magnetic fields.

Abstract

We derive an explicit matrix representation for the Hamiltonian of the Ising model in mutually orthogonal external magnetic fields, using as basis the eigenstates of a system of non-interacting \mbox{spin~$1/2$} particles in external magnetic fields. We subsequently apply our results to obtain an analytical expression for the ground state energy per spin, to the fourth order in the exchange integral, for the Ising model in perpendicular external fields.