We analyze in detail, beyond the usual scaling hypothesis, the finite-size convergence of static quantities toward the thermodynamic limit. In this way, we are able to obtain sequences of pseudo-critical points, which display a faster convergence rate as compared to currently used methods. The approaches are valid in any spatial dimension and for any value of the dynamic exponent. We demonstrate the effectiveness of our methods both analytically, on the basis of the one dimensional X Y model, and numerically, considering c= 1 transitions occurring in nonintegrable spin models. In particular, we show that these general methods are able to precisely locate the onset of the Berezinskii–Kosterlitz–Thouless transition making only use of ground-state properties on relatively small systems.
American Physical Society
9 Apr 2008
Volume: 77 Issue: 15 Pages: 155413
Physical Review B