Surajit Sen and James Christopher Phillips. Asymptotic behavior of dynamical correlations via perturbative analysis of infinite continued fractions. Physical Review E 47(5):3152-3157, 1993.

The continued-fraction formalism demonstrates that the Laplace-transformed dynamical correlations can be expressed as infinite continued fractions (ICF's). We propose a generalization of the dynamical convergence method (GDCM) of J. Hong and M. H. Lee `Phys. Rev. Lett. 55, 2375 (1985)' of perturbatively evaluating insoluble ICF's when a closely related ICF is exactly soluble. The proposed method overcomes an existing limitation of the dynamical convergence method which involves accurate computing of ratios of small numbers. The limitations are surmounted by exploiting an ''inversion'' property of ICF's. The GDCM allows computationally fast and simple perturbative evaluation of insoluble ICF's with up to 10(xi), xi less-than-or-equal-to 6, levels of the insoluble ICF when a related ICF is soluble. The method appears to be appropriate for studies of asymptotic behavior of dynamical correlations described by slowly converging and nonconverging ICF's, which are otherwise insoluble, when closely related soluble ICF's exist. The desirable feature of the GDCM is that the computation times required to solve the ICFs are unrelated to the details of the convergence properties. The method has been applied to recalculate the dynamical-spin pair correlation of a recently studied classical XX spin cluster. This application is described in this work.