Attractive Hubbard model in the strong-coupling regime. Relation between transition temperature, magnetic penetration depth and gap

Motivated by the empirically established universal trends and correlations in the properties of extreme type-II superconductors, we explore the occurrence of analogous behavior in the strong-coupling regime of the three-dimensional Hubbard model with attractive on-site interaction. In this limit we derive scaling relations between the transition temperature, the zero-temperature gap and the penetration depth. We observe a remarkable agreement with the empirical trends. Certain limitations may be attributed to the neglect of charge-density fluctuations. © 1993.