Critical Behavior of the Isotropic Ferromagnetic Quantum Heisenberg Chain

The thermodynamic Bethe-Ansatz equations for the isotropic ferromagnetic $S=\frac{1}{2}$ Heisenberg chain have been solved numerically. At low temperatures, I find a power-law dependence on $T$ for the specific heat and the susceptibility with critical exponents $\alpha =-0.49\mathrm{}\pm 0.02$, $\gamma =2.00\mathrm{}\pm 0.02$, and $\Delta \simeq \gamma$. The exponent $\alpha$ is compatible with effective spin waves and $\gamma$ and $\Delta$ are the exponents of the classical chain. Amplitudes and corrections to scaling are obtained and differences with previous results are discussed.