Matrix products with applications to classical statistical mechanics, 1. Reflectivity of onedimensional solids, 2
Abstract
A matrix product that generalizes the Kronecker product (the direct product of matrices) is introduced. Numerous theorems concerning the properties of this matrix product and its relationships with Kronecker, Hamard, and regular matrix multiplication are stated and proved. Its application to the study of models in classical statistical mechanics that have one and twobody interactions is demonstrated in the mapping from a specialized BlumeEmeryGriffithsRys spin one model to a spin 1/2 Ising model with a temperature dependent magnetic field. Also a model that is a combination of a onedimensional and mean field model is introduced and discussed. An apparatus and technique developed to obtain the visible and near infrared polarized reflectivity spectra of small (tenths of a millimeter) single crystals is described. The polarized room temperature single crystal reflectivity of three classes of quasionedimensional compounds is analyzed.
 Publication:

Ph.D. Thesis
 Pub Date:
 1978
 Bibcode:
 1978PhDT........12N
 Keywords:

 Matrices (Mathematics);
 Particle Spin;
 Polarization (Charge Separation);
 Reflectance;
 Single Crystals;
 Statistical Mechanics;
 Charge Transfer;
 Ferromagnetism;
 Magnetic Fields;
 Spectrophotometers;
 Spectrum Analysis;
 SolidState Physics