Critical Exponents of the Heisenberg Spin Chain

Andreas Klümper

R. BISCHOF, Wolfhard Janke E

Kazuo Hida

The critical exponents of the phase transitions in the ground state of the ferromagnetic-antiferromagnetic alternating spin-1/2 Heisenberg chain are determined by means of the numerical diagonalization with emphasis on the boundary between the Haldane phase and the large- D phase. It is found that this phase boundary is a line of continuously varying critical exponents. The results are in agreement with the series expansion results by Yamanaka, Hatsugai and Kohmoto.

P. Schlottmann

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 $\ensuremath{\alpha}=\ensuremath{-}0.49\ifmmode\pm\else\textpm\fi{}0.02$, $\ensuremath{\gamma}=2.00\ifmmode\pm\else\textpm\fi{}0.02$, and $\ensuremath{\Delta}\ensuremath{\simeq}\ensuremath{\gamma}$. The exponent $\ensuremath{\alpha}$ is compatible with effective spin waves and $\ensuremath{\gamma}$ and $\ensuremath{\Delta}$ are the exponents of the classical chain. Amplitudes and corrections to scaling are obtained and differences with previous results are discussed.

Carlo Heissenberg, Augusto Sagnotti

P. Schlottmann, Kong-Ju-Bock Lee