Thermodynamic scaling functions in the critical region of type-II superconductors

A recently proposed nonperturbative method for evaluation of the thermodynamic scaling functions in the nominal critical region of quasi-two-dimensional type-II superconductors is generalized and extended to arbitrary type-II systems. It is found that, in general, layered superconductors do not exhibit single-parameter scaling except in two opposite limits corresponding to two-dimensional (2D) and (an) isotropic 3D systems. Explicit, closed-form expressions for the scaling functions are constructed in these two limits. The results are found to be in good agreement with experiments and Monte Carlo simulations. The limits on the applicability of the Landau level description of fluctuations are also discussed.