Thermodynamics of two component bosons in one dimension

On the basis of Bethe ansatz solution of two-component bosons with SU(2) symmetry and delta-function interaction in one dimension, we study the thermodynamics of the system at finite temperature by using the strategy of thermodynamic Bethe ansatz (TBA). It is shown that the ground state is an isospin ferromagnetic state by the method of TBA, and at high temperature the magnetic property is dominated by Curie's law. We obtain the exact result of specific heat and entropy in strong coupling limit which scales like T at low temperature. While in weak coupling limit, it is found there is still no Bose-Einstein Condensation (BEC) in such 1D system.