Specific heat and high-temperature series of lattice models: Interpolation scheme and examples on quantum spin systems in one and two dimensions

We have developed a method for evaluating the specific heat of lattice spin systems. It is based on the knowledge of high-temperature series expansions, the total entropy of the system, and the low-temperature expected behavior of the specific heat as well as the ground-state energy. By the choice of an appropriate variable (entropy as a function of energy), a stable interpolation scheme between low and high temperature is performed. Contrary to previous methods, the constraint that the total entropy is $\mathrm{log}(2S+1)$ for a spin S on each site is automatically satisfied. We present some applications to quantum spin models on one- and two-dimensional lattices. Remarkably, in most cases, a good accuracy is obtained down to zero temperature.