Lattice Investigations into Phenomena of Critical Phase Transition Temperatures

摘要

The properties of the spin 1/2 Ising model have been investigated on a regular three dimensional lattice of coordination three and two related lattices. These three lattices are the three dimensional analogues of the honeycomb, triangular and kagome lattices. Hence star-triangle relations have been used to advantage. Both high and low temperature expansions of standard thermodynamic quantities have been obtained. The XY model of a quantum lattice fluid has been studied by the method of high temperature expansion. Several lattice statistical models have been cast in the form of interacting fermion problems. Phase diagrams for Ising models with antiferromagnetic second neighbor interactions have been studied and the exact phase transition interaction ratio at zero temperature has been found for a variety of special cases. (Author)