ABSTRACT
This chapter reviews the various techniques developed for the study of the thermodynamics of integrable systems at the example of the simplest one, namely the spin-12 Heisenberg chain. As a matter of fact, the strict ground state is inaccessible due to the very fundamentals of thermodynamics. The minimization of the free energy functional yields what is known as the thermodynamical Bethe ansatz. Application of thermodynamical data of quantum spin chains is the microscopic modelling of magnetic systems such as spin-Peierls compounds and ladder systems. The microscopic interactions of a given substance are determined by a comparative analysis of the experimental results for the susceptibility and the theoretical data obtained for a model. Lowering the temperature, the systems enter a large regime with non-universal correlations and finally approach the quantum critical point at exactly zero temperature showing again universal yet nontrivial properties with divergent correlation lengths governed by conformal field theory.
