Low-temperature behavior of the S=(1/2) ferromagnetic Heisenberg chain

A detailed account of the results of the numerical solution of the thermodynamic Bethe-ansatz equations for the isotropic ferromagnetic S=(1/2) Heisenberg chain is presented. The extrapolation procedure used in approximating the infinite set of coupled nonlinear integral equations is discussed. The data for the truncated integral equations are analyzed in terms of a finite-string-size scaling. Analytic expressions for the free energy and susceptibility for T→0 are obtained. All the results are consistent with entropy S∼(T/‖J‖${)}^{1/2}$ and χ∼ ‖J‖ / $T^2$ [${\mathrm{scrL}}^{\mathrm{-}1}$+(lnscrL)/${\mathrm{scrL}}^2$+...]+O ($T^{\mathrm{-}3/2}$) , where scrL=ln(‖J‖/T), suggesting the existence of a marginal variable. The logarithmic corrections reflect the analogy to the Kondo problem.