Competition between the finite size and the disorder effects in rectangular superconducting small grains for hole-doped cuprates by use of a model based on spin fluctuations

In this article, we consider rectangular superconducting small grains for hole-doped cuprates near diagonal zone. Since important models for high temperature superconductivity contain the exchange of spin fluctuations, we want to apply one of the famous of them named spin-fermion model. In the framework of this model, we want to obtain the total polarization (without considering self-energy and using standard Eliashberg equations) and first order correction of polarization (using perturbed linearized equation and normal and anomalous first order Green's function) in terms of finite size and disorder effects, numerically. It's worth mentioning that the first order perturbed polarization is expanded in terms of size-dependent gap and this polarization itself depends on disorder. Finally, competition between two effects is investigated and it is observed that the finite size effect is so dominant with respect to the disorder effect.