Exact eigenvalues of the Ising Hamiltonian in one-, two- and three-dimensions in the absence of a magnetic field

@article{citeulike:2175581, abstract = {The Hamiltonian of the Ising model in one-, two- and three-dimensions has been analysed using unitary transformations and combinatorics. We have been able to obtain closed formulas for the eigenvalues of the Ising Hamiltonian for an arbitrary number of dimensions and sites. Although the solution provided assumes the absence of external magnetic fields an extension to include a magnetic field along the z-axis is readily extracted. Furthermore, generalisations to a higher number of spin components on each site are possible within this method. We made numerical comparisons with the partition function from the earlier analytical expressions known in the literature for one- and two-dimensional cases. We find complete agreement with these studies.}, author = {Dixon, J. M. and Tuszynski, J. A. and Nip, M. L. A. }, citeulike-article-id = {2175581}, comment = {* Eigendecomposition of the path graph}, doi = {10.1016/S0378-4371(00)00318-6}, journal = {Physica A: Statistical Mechanics and its Applications}, keywords = {ising, physics}, month = {January}, number = {1-2}, pages = {137--156}, posted-at = {2007-12-27 18:35:01}, priority = {2}, title = {Exact eigenvalues of the Ising Hamiltonian in one-, two- and three-dimensions in the absence of a magnetic field}, url = {http://dx.doi.org/10.1016/S0378-4371(00)00318-6}, volume = {289}, year = {2001} }

TY - JOUR ID - citeulike:2175581 L3 - citeulike-article-id:2175581 TI - Exact eigenvalues of the Ising Hamiltonian in one-, two- and three-dimensions in the absence of a magnetic field JF - Physica A: Statistical Mechanics and its Applications VL - 289 IS - 1-2 SP - 137 EP - 156 N2 - The Hamiltonian of the Ising model in one-, two- and three-dimensions has been analysed using unitary transformations and combinatorics. We have been able to obtain closed formulas for the eigenvalues of the Ising Hamiltonian for an arbitrary number of dimensions and sites. Although the solution provided assumes the absence of external magnetic fields an extension to include a magnetic field along the z-axis is readily extracted. Furthermore, generalisations to a higher number of spin components on each site are possible within this method. We made numerical comparisons with the partition function from the earlier analytical expressions known in the literature for one- and two-dimensional cases. We find complete agreement with these studies. KW - ising KW - physics N1 - * Eigendecomposition of the path graph AU - Dixon, JM AU - Tuszynski, JA AU - Nip, MLA PY - 2001/01/01/ UR - http://dx.doi.org/10.1016/S0378-4371(00)00318-6 ER -