Nearly universal crossing point of the specific heat curves of Hubbard models

Abstract

A nearly universal feature of the specific heat curves C(T,U) vs. T for different U of a general class of Hubbard models is observed. That is, the value C_+ of the specific heat curves at their high-temperature crossing point T_+ is almost independent of lattice structure and spatial dimension d, with C_+/k_B \approx 0.34. This surprising feature is explained within second order perturbation theory in U by identifying two small parameters controlling the value of C_+: the integral over the deviation of the density of states N(\epsilon) from a constant value, characterized by \delta N=\int d\epsilon |N(\epsilon)-1/2|, and the inverse dimension, 1/d.