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

TL;DR

The paper identifies a nearly universal crossing point in the specific heat curves of Hubbard models, showing that the specific heat at this point is almost independent of lattice structure and dimension, explained via perturbation theory.

Contribution

It reveals a universal crossing point in specific heat curves of Hubbard models and explains this phenomenon using second order perturbation theory.

Findings

The specific heat crossing point C_+ is approximately 0.34 k_B.

C_+ is nearly independent of lattice structure and dimension.

The phenomenon is explained by two small parameters: deviation in density of states and inverse dimension.

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.