Finite-size scaling in the ground state of spin-1/2antiferromagneticXXZrings

Convincing evidence that the correlation function ω(l,N)=4〈$S_i^x$ $S_{i+l}^x$〉 obeys finite-size scaling for the XY model is obtained from large rings (number of spins N up to ≊1000). ω(l,N) for the Heisenberg model behaves much like the XY model for the small N’s available (up to 18), suggesting finite-size scaling in the Heisenberg model. The scaling function, f(l/N)≊ω(l,N)/ω(l,∞), seems to show the remarkable property $f_{\mathrm{Heis}\left(\mathrm{y}\right)=\left[f_{\mathrm{XY}}\right(\mathrm{y}{\left)\right]}^{\alpha }}$, with α≊1.75. Also, α appears to vary smoothly with the exchange-parameter ratio γ=$J_{\mathrm{xx}}$/$J_{\mathrm{zz}}$. The scaling assumption is used to estimate ω(l,∞).