Exact Solutions to Special High Dimensional O(n) Models, Dimensional Reductions, gauge redundancy, and special Frustrated Spin and Orbital models

摘要

This work addresses models (e.g. potential models of directed orbitalsystems- the manganates) in which an effective reduction dimensionality occursas a result of a new symmetry which is intermediate between that of global andlocal gauge symmetry. This path towards dimensional reduction is examined insimple O(n) spin models and lattice gauge theories. A high temperatureexpansion is employed to map special anisotropic high dimensional models intolower dimensional variants. We show that it is possible to have an effectivereduction in the dimension without the need of compactifying some dimensions.These models are frustrated and display a symmetry intermediate between localand global gauge symmetries. Some solutions are presented. Our dimensionalreductions are a generlization of the trivial dimensional reduction that occurin pure two dimensional gauge theories. It will be further seen that theabsence of a ``phase interference'' effect plays an important role in highdimensional problems. By identifying another (``permutational'') symmetrypresent in the large n limit, we will further show how to generally map globalhigh dimensional spin systems onto a one dimensional chain and discussimplications.