46 research outputs found
Unitary Matrix Models and Phase Transition
We study the unitary matrix model with a topological term. We call the
topological term the theta term. In the symmetric model there is the phase
transition between the strong and weak coupling regime at . If
the Wilson term is bigger than the theta term, there is the strong-weak
coupling phase transition at the same . On the other hand, if the
theta term is bigger than the Wilson term, there is only the strong coupling
regime. So the topological phase transition disappears in this case.Comment: 9 pages, LaTeX, Comments about the topological phase transition are
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Unitary Matrix Models and Painlev\'{e} III
We discussed the full unitary matrix models from the view points of
integrable equations and string equations. Coupling the Toda equations and the
string equations, we derive a special case of the Painlev\'{e} III equation.
From the Virasoro constrains, we can use the radial coordinate. The relation
between and is like the complex conjugate. %An implicit to the
fusion of topological sigma model %is therby expected.Comment: 10 pages, LaTeX, final version to appear in Mod. Phys. Lett.