eng Science and Education Publishing International Journal of Physics 2333-4576 2019-01-18 7 1 6 15 10.12691/ijp-7-1-2 IJP2019712 article Explicit Matrix Representation for the Hamiltonian of the One Dimensional Spin 1/2 Ising Model in Mutually Orthogonal External Magnetic Fields Kunle Adegoke 1 Henry Otobrise 2 Tolulope Famoroti 2 Adenike Olatinwo solakunle711@yahoo.com 2 Funmi Akintujoye 2 Afees Tiamiyu 2 Department of Physics and Engineering Physics, Obafemi Awolowo University, 220005 Ile-Ife, Nigeria Department of Basic Sciences, Lead City University, Ibadan, Nigeria 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. http://pubs.sciepub.com/ijp/7/1/2/ijp-7-1-2.pdf ising model quantum fluctuations is non-degenerate non-degenerate rayleigh-schr?dinger perturbation theory