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 allows us to derive a set of nonlinear integral equations for the thermodynamics of these spin chains. We provide numerical solutions of these integral equations for the entropy as a function of magnetic field, temperature and the coupling constant. In addition we describe, at low but finite temperature, the possible scenarios for the ground state diagram for high-spin chain and longer range interchain interactions.