RENORMALIZATION-GROUP APPROACH TO ANISOTROPIC SUPERCONDUCTORS AT FINITE-TEMPERATURE

A renormalization-group (RG) analysis of the superconductive instabili ty of an anisotropic fermionic system is developed at a finite tempera ture. The method appears as a natural generalization of Shankar's appr oach to interacting fermions and of Weinberg's discussion about anisot ropic superconductors at T=0. The need of such an extension is fully j ustified by the effectiveness of the RG at the critical point. Moreove r the relationship between the RG and a mean-field approach is clarifi ed, and a scale-invariant gap equation is discussed at a renormalizati on level in terms of the eigenfunctions of the interaction potential, regarded as the kernel of an integral operator on the Fermi surface. A t the critical point, the gap function is expressed by a single eigenf unction and no symmetry mixing is allowed. As an illustration of the m ethod we discuss an anisotropic tight-binding model for some classes o f high-T-c, cuprate superconductors, exhibiting a layered structure. S ome indications on the nature of the pairing interaction emerge from a comparison of the model predictions with the experimental data.