  We study the finite-size scaling (FSS) property of the correlation ratio, the
ratio of the correlation functions with different distances. It is shown that
the correlation ratio is a good estimator to determine the critical point of
the second-order transition using the FSS analysis. The correlation ratio is
especially useful for the analysis of the Kosterlitz-Thouless (KT) transition.
We also present a generalized scheme of the probability-changing cluster
algorithm, which has been recently developed by the present authors, based on
the FSS property of the correlation ratio. We investigate the two-dimensional
quantum XY model of spin 1/2 with this generalized scheme, obtaining the
precise estimate of the KT transition temperature with less numerical effort.
