Static and Dynamic Real-space Renormalization Through Series Expansions For Correlation-functions

The renormalization-group analysis of correlation-function series expansions introduced by Stella et al. for computing the static critical properties of lattice-spin systems is refined by employing an additional interaction variable, and extended to dynamical critical phenomena. The static approach is applied to the square-lattice Ising model with nearest-neighbor and diagonal interactions, with use of the original high-temperature series to ninth order for pair-correlation functions. The critical point, the thermal and magnetic exponent, and the leading correction-to-scaling exponent are computed. Applications of the method to the spin-(1/2) Ising and XY models in two and three dimensions are also reviewed. The possibility of basing a dynamical renormalization approach on this type of analysis is shown. The new dynamical method, which avoids proliferation of interactions and memory effects, is applied to the square-lattice Glauber model. The study of original series for pair relaxation times (to eigth order in the nearest-neighbor interaction and to fourth order in the diagonal one) gives estimates of the dynamic exponent z.