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We report on a study of the superconducting order parameter thermodynamicfluctuations in $\mathrm{YBa}_2\mathrm{Cu}_3\mathrm{O}_{7 - \delta}$,$\mathrm{Bi}_{2}\mathrm{Sr}_{2}\mathrm{CaCu}_{2}\mathrm{O}_{8+ \delta}$ and$\mathrm{KOs}_2\mathrm{O}_6$ compounds. A non-perturbative technique within theframework of the renormalized Gaussian approach is proposed. The essentialfeatures are reported (analytically and numerically) through Ginzburg-Landau(GL) model-based calculations which take into account both the dimension andthe microscopic parameters of the system. By presenting a self-consistentapproach (SCA) improvement on the GL theory, a technique for obtainingcorrections to the asymptotic critical behavior in terms of non universalparameters is developed. Therefore, corrections to the specific heat and thecritical transition temperature for one-, two- and three-dimensional samplesare found taking into account the fact that fluctuations occur at all lengthscales as the critical point of a system is approached. The GL model in thefree-field approximation and the 3D-XY model are suitable for describing theweak and strong fluctuation regimes respectively. However, with a modifiedquadratic coefficient, the renormalized GL model is able to explain certainexperimental observations including the specific heat of complicated systems,such as the cuprate superconductors and the $\beta$-pyrochlore oxides. It isclearly shown that the enhancement, suppression or rounding of the specificheat jump of high-$T_c$ cuprate superconductors at the transition areindicative of the order parameter thermodynamic fluctuations according to thedimension and the nature of interactions.

physical review. e

Effects of critical fluctuations and dimensionality on the jump in  specific heat at the superconducting transition temperature: Application to  YBa2Cu_3 O_7 - \delta, Bi_2 Sr_2CaCu_2 O_8+\delta and KOs_2 O_6 compounds