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

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₊/kB≈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(ε) from a constant value, characterized by δN=∫dε|N(ε)-1/2|; and the inverse dimension $1/d.$