  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.

Strongly Correlated Electrons