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We analyzed the non-Fermi behavior of copper oxides superconductors with an energy-dependent density of states of the van Hove (logarithmic) form, using the model proposed by Anderson and Yin and Chakravarty. The critical temperature degradation, due to a small amount of non-magnetic impurities, is also analyzed. It is shown that the decrease of the critical temperature is not of the Abrikosov–Gorkov type.

We study the behavior of the finite temperature quantum nonlinear sigma model in two dimensions in the presence of the damping of the form $$f (|\omega_n|) = \gamma |\omega_n|^\alpha$$ , where α satisfies $$\alpha \ge 1$$ . The analytical calculations will be performed using $$\alpha = 2$$ and the results will be compared with the standard results obtained for the standard quantum nonlinear sigma model. The behavior of such a system is connected with the pseudogap which appears in the normal state of the cuprate superconductors.

We analyze the two-dimensional antiferromagnet with a quantum disordered ground state and a gap to bosonic excitations with finite spin. The zero temperature (T = 0) quantum phase transition is studied, and the finite temperature effects are also considered in the low temperature approximation of the Renormalization Group Method. The violation of the universality expected for d = 2 system has been shown to be logarithmic for T = 0 and T ≠ 0. We showed that chemical potential and the ground state energy depends on the interaction parameters at T = 0 and T ≠ 0. but this dependence is logarithmic.

The electrical conductivity of a two-dimensional disordered system has been calculated taking into consideration an exponential density of states. The effect of backscattering has been calculated. For an exponential density of states the diffusion pole has been removed. In the Ω→0 limit we showed that there exists a critical concentration that corresponds to the transition point from the metallic to the insulating phase.

The exchange enhancement of electron-phonon coupling has been calculated for a three- and two-dimensional superconductor. The critical temperature has been determined taking into consideration the electron-phonon attraction, the spin fluctuations effect, and Coulomb repulsion. The two-dimensional spin fluctuations and Coulomb contributions were calculated. TheTc dependence on the productUN(0) has been analyzed in both the three- and two-dimensional cases.

Using the Eliashberg equations for superconductivity in a quasi-3D high-temperature super-conductor, taking into consideration the¯q-dependent phonon-mediated electron-electron interaction, the effect of the disordered magnetic correlations, and Coulomb repulsion affected by disorder, we calculated the expression for the critical temperature. The phonon and the magnetic kernels have a logarithmic divergence and the critical temperature differs from the McMillan form. The Coulomb repulsion in the presence of disorder has been estimated. The disordered magnetic correlations can decrease the critical temperature or can suppress the superconductivity. The effect of various parameters on the decrease of the critical temperature has been analyzed.

Using the Eliashberg equations for superconductivity in a layered high-temperature superconductor and taking into consideration the phonon-mediated electron-electron interaction and the effect of the disordered magnetic correlations, we calculated the expressions for the critical temperature. The phonon and the magnetic kernels have a logarithmic divergence in the lowfrequency limit and the critical temperature differs from the McMillan form. The effect of various parameters on the decrease of the critical temperature has been analyzed. The renormalization functionZ ph (ω) contains a logarithmic dependence onω.

Using the Eliashberg equations, we calculated the critical temperature of a two-dimensional superconductor with strong disorder. The retarded Coulomb interaction and the magnetic correlations have been included in the renormalization function Z(ω). The critical temperature decreases with the concentration of impurities, in agreement with the experiments.

The effect of disorder and magnetic correlations is considered in connection with the occurrence of the superconducting state. The effect of disorder can reduce the pair-weakening parameter. The Coulomb pseudopotential is strongly dependent on disorder and decreases drastically the critical temperature. The competition between disorder and magnetic correlation effects is analyzed.

The effect of disorder on the phononic plasmonic microscopic model for high-critical-temperature superconductors has been studied. The dynamic screening of the Coulomb interaction due to the disorder results in a decrease in T{sub c}. For a two-dimensional electronic system the plasmon modes are strongly affected by disorder. Taking this efect into consideration, we show that T{sub c} can decrease but there is also an additional effect to the phonon-plasmon attractive contribution. 25 refs.

The influence of magnetic correlations and disorder in a two-dimensional Fermi liquid is considered in connection with the occurrence of the superconducting state. The disorder effect and magnetic correlations work against the superconducting state but at the same time are competitive phenomena. We show that the critical temperature can decrease due to the magnetic correlations and disorder, but the effect of correlations is reduced by the disorder. The electronic mass enhancement has been calculated taking into consideration the magnetic correlation effects and disorder. Its dependence on the concentration impurities, in agreement with the experimental data, shows the importance of the localization effects due to disorder. These results are in agreement with the experimental data obtained for the high critical temperature superconductors.