In the search for exotic properties of spin lattices, many numerical methods focus on the ground state and on the low-energy excitations of a model. Here, we use the opposite approach, with high temperature series expansions. The coefficients of the free energy, the specific heat or the magnetic susceptibility series are obtained up to 20 (depending on the model complexity). Yet, the convergence radius limits the range of temperature where information can be obtained by simple summation. Thus, alternative methods are required. One of them is the entropy method, that uses some hypothesis on the nature of the ground state to reconstruct thermodynamic quantities over the whole temperature range.
The entropy method has been used on several compounds to propose exchange parameter values. When a finite temperature phase transition occurs, a singularity forbids to use the entropy method, but then, information about the critical exponents and about the critical temperature can be extracted. I will present a review of these methods and their limitations, together with some applications.
