Scaling and Duality in the Superconducting Phase Transition

The renewed interest for critical fluctuations in superconductors is due to the enormous variety of interesting phenomena observed in the last decade. In a zero external field regime, non-classical values of the critical exponents and amplitude ratios were measured. In the observed critical region we have −0.03 < α < 0, ν ≈ 0.67 and A+/A− ≈ 1.065. These values were measured for bulk samples of YBa2Cu3O7−δ (YBCO). They indicate that the observed critical region corresponds to the XY universality class. In the non-zero field regime, the thermal fluctuations make the vortex lattice melt. For high fields this transition is known to be of first-order. Most thermal fluctuation effects in superconductors can be understood using the Ginzburg-Landau (GL) model. In zero field, the GL model is given by