Abstract
Considering in symmetrical half-length bond operations, we present in this paper two types of newly-developed generalizations of the remarkable Migdal-Kadanoff bond-moving renormalization group transformation recursion procedures. The predominance in application of these generalized procedures are illustrated by making use of them to study the critical behavior of the spin-continuous Gaussian model constructed on the typical translational invariant lattices and fractals respectively. Results such as the correlation length critical exponents obtained by these means are found to be in good conformity with the classical results from other previous studies.
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