Spin-(1/2 antiferromagneticXXZchain: New results and insights

Abstract

We study the criticality at the isotropic limit of the S=(1/2, antiferromagnetic, XXZ chain on approach from the Ising side. Long series are developed for the longitudinal and transverse correlation sums or structure factors $S_{\mathrm{zz}}$ and $S_{+\mathrm{-}}$ around the Ising limit. Their extrapolation indicates a divergence as the critical point is approached, with two different powers, a result quite unexpected if one employs a naive scaling argument since the critical correlations are isotropic and there is only one correlation length, ξ. An analytical calculation is presented, in which this paradox is resolved and the numerical results are confirmed.