Thermodynamics of quantum Heisenberg spin chains

Thermodynamic properties of the quantum Heisenberg spin chains with $S=1/2,$ 1, and $3/2$ are investigated using the transfer-matrix renormalization-group method. The temperature dependence of the magnetization, susceptibility, specific heat, spin-spin correlation length, and several other physical quantities in a zero or finite applied field are calculated and compared. Our data agree well with the Bethe ansatz, exact diagonalization, and quantum Monte Carlo results and provide further insight into the quantum effects in the antiferromagnetic Heisenberg spin chains.