A simple analytic theory of thermodynamics at finite temperature for the spin-1/2 antiferromagnetic Heisenberg chain is proposed based on the picture of the particle-hole pair excitations. The dispersion relation of the particle-hole pairs is derived in the formulation of thermodynamic Bethe ansatz provided that the particles and holes have the same energy and they are excited as normal modes. It is shown that the behaviour of the specific heat is in excellent agreement with the numerical and experimental results.
The numerical solution of the Bethe ansatz equations of an integrable SU(2)-invariant generalization of the spin-S antiferromagnetic Heisenberg chain (Takhtajian-Babujian model) with a spin-S' impurity in zero magnetic field is presented. The entropy, specific heat and susceptibility of an impurity of spin S' are obtained numerically as a function of the spin S of the chain. Three situations have to be distinguished: (i) if S'=S the impurity just corresponds to one more site in the chain; (ii) if S'>S the impurity spin is only partially compensated (undercompensated) at T=0, leaving an effective spin of (S'-S); (iii) if S'