Geometrical Origin of Tricritical Points of various U(1) Lattice Models
Abstract
We review the dual relationship between various compact U(1) lattice models and Abelian Higgs models, the latter being the disorder field theories of linelike topological excitations in the systems. We point out that the predicted firstorder transitions in the Abelian Higgs models (ColemanWeinberg mechanism) are, in three dimensions, in contradiction with direct numerical investigations in the compact U(1) formulation since these yield continuous transitions in the major part of the phase diagram. In four dimensions, there are indications from Monte Carlo data for a similar situation. Concentrating on the strongcoupling expansion in terms of geometrical objects, surfaces or lines, with certain statistical weights, we present semiquantitative arguments explaining the observed crossover from firstorder to continuous transitions by the balance between the lowest two weights (``2:1 ratio'') of these geometrical objects.
 Publication:

arXiv eprints
 Pub Date:
 April 1995
 arXiv:
 arXiv:heplat/9504010
 Bibcode:
 1995hep.lat...4010J
 Keywords:

 High Energy Physics  Lattice
 EPrint:
 LaTeX and figure files, http://www.physik.fuberlin.de/kleinert.html