Matrix model approach to the flux-lattice melting in two-dimensional superconductors.

We investigate a gauged matrix model in the large-{ital N} limit that is closely related to the superconductor fluctuation and the flux-lattice melting in two dimensions. With the use of the saddle-point method, the free energy is expanded up to eighth order for the coupling constant {ital g}. In the case that the coefficient of the quadratic term of the Ginzburg-Landau matrix model is negative, a critical point {ital g}={ital g}{sub {ital c}} is obtained in the large-{ital N} limit and the relation between this phase transition and the two-dimensional flux-lattice melting transition is discussed.