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

We investigate a gauged matrix model in the large-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 g. In the case that the coefficient of the quadratic term of the Ginzburg-Landau matrix model is negative, a critical point g=gc is obtained in the large-N limit and the relation between this phase transition and the two-dimensional flux-lattice melting transition is discussed