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Temperature dependence of the magnetization of the Haldane spin chain atfinite magnetic field is analyzed systematically. Quantum Monte Carlo dataindicates a clear minimum of magnetization as a function of temperature in thegapless regime. On the basis of the Tomonaga-Luttinger liquid theory, we arguethat this minimum is rather universal and can be observed for general axiallysymmetric quasi-one-dimensional spin systems. Our argument is confirmed by themagnetic-field dependence of the spin-wave velocity obtained numerically. Onecan estimate a magnitude of the gap of any such systems by fitting theexperimental data with the magnetization minimum.Comment: 9 pages, 7 figure

Universal Temperature Dependence of the Magnetization of Gapped Spin Chains