Thermodynamics of quantum spin chains with competing interactions

We consider integrable quantum spin chains with competing interactions. We apply the quantum transfer matrix approach to these spin chains. This allowed us to derive a set of non-linear integral equations for the thermodynamics of these spin chains. We provide numerical solution of these integral equations for the entropy as function of magnetic field, temperature and the coupling constant. This allow us to assess, at low but finite temperature, the picture describing the ground state diagram for high spin chain and longer range interchain interactions.