Scaling critical behavior of superconductors at zero magnetic field

We consider the scaling behavior in the critical domain of superconductors at zero external magnetic field. The first part of the paper is concerned w ith the Ginzburg-Landau model in the zero-magnetic-field Meissner phase. We discuss the scaling behavior of the superfluid density and we give an alte rnative proof of Joseph son's relation for a charged superfluid. This proof is obtained as a consequence of an exact renormalization group equation fo r the photon mass. We obtain Josephson's relation directly in the form rho( s) similar to t(v); that is, we do not need to assume that the hyperscaling relation holds. Next, we give an interpretation of a recent experiment per formed in thin films of YBa2Cu3O7 - delta. We argue that the measured mean- field-like behavior of the penetration depth exponent v' is possibly associ ated with a nontrivial critical behavior and we predict the exponents v = 1 and alpha = -1 for the correlation length and specific heat, respectively. In the second part of the paper we discuss the scaling behavior in the con tinuum dual Ginzburg-Landau model. After reviewing lattice duality in the G inzburg-Landau model, we discuss the continuum dual version by considering a family of scalings characterized by a parameter zeta introduced such that m(h,0)(2) similar to t(zeta), where m(h,0) is the bare mass of the magneti c induction field. We discuss the difficulties in identifying the renormali zed magnetic induction mass with the photon mass. We show that the only way to have a critical regime with v' = v' approximate to 2/3 is having zeta a pproximate to 4/3, that is, with m(h,0) having the scaling behavior of the renormalized photon mass. [S0163-1829(99)03130-6].