Explicit Matrix Representation for the Hamiltonian of the One Dimensional Spin 1/2 Ising Model in Mutually Orthogonal External Magnetic Fields

Kunle Adegoke¹, Henry Otobrise², Tolulope Famoroti¹, Adenike Olatinwo^1, , Funmi Akintujoye¹ and Afees Tiamiyu¹

¹Department of Physics and Engineering Physics, Obafemi Awolowo University, 220005 Ile-Ife, Nigeria

²Department of Basic Sciences, Lead City University, Ibadan, Nigeria

Cite this paper:
Kunle Adegoke, Henry Otobrise, Tolulope Famoroti, Adenike Olatinwo, Funmi Akintujoye and Afees Tiamiyu. Explicit Matrix Representation for the Hamiltonian of the One Dimensional Spin 1/2 Ising Model in Mutually Orthogonal External Magnetic Fields. International Journal of Physics. 2019; 7(1):6-15. doi: 10.12691/ijp-7-1-2

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 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.

Keywords:
ising model quantum fluctuations is non-degenerate non-degenerate rayleigh-schrödinger perturbation theory

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