A linearized version of the Hartree-Fock method is reinvestigated in order to develop a new technique for the study of phase transitions. This is studied with reference to an exactly soluble model, yielding excellent results.NUCLEAR STRUCTURE Phase transitions. Approximate many body methods applied to a soluble model.

Physical Review CDec 1, 19824 citations

Physica A Statistical Mechanics and its Applications

Exactly soluble model of phase transition with cubic anisotropy

Nikolay M. Plakida, Andrzej Radosz, N. S. Tonchev

Published May 1, 1987• 5 citations

Publisher

DOI: 10.1016/0378-4371(87)90065-3

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Exactly soluble spin-

\frac{1}2

models on three-dimensional lattices are proposed by generalizing Kitaev model on honeycomb lattice to three dimensions with proper periodic boundary conditions. The simplest example is spins on a diamond lattice which is exactly soluble. The ground state sector of the model may be mapped into a p-wave paired state on cubic lattice. We observe for the first time a topological phase transition from a gapless phase to a gapped phase in an exactly soluble spin model. Furthermore, the gapless phase can not be gapped by a perturbation breaking the time reversal symmetry. Unknotted and unlinked Wilson loops arise as eigen excitations, which may evolute into linked and knotted loop excitations. We show that these closed string excitations obey abelian statistics in the gapped phase and non-abelian statistics in the gapless phase.