Thermodynamics of the Limiting Cases of the XXZ Model Without Bethe Ansatz

The Heisenberg XXZ model is a chain model with nearest-neighbor interactions. Its thermodynamics is exactly obtained via Bethe ansatz. Recently, we developed a method to derive the hightemperature expansion of the grand potential per site of translationally invariant chain models, with periodic boundary conditions. Here we apply this approach to the XXZ model with periodic boundary conditions for the Ising limit case (t = 0) and the free fermion case ( = 0 and h = 0), obtaining results in agreement with the literature. In this new way of obtaining the coeÆcients of the high-temperature expansion of the grand potential, the coeÆcients are derived from an auxiliary function written only in terms of open connected sub-chains.