Positive-function renormalization group

III. Stretched-Exponential Scaling and the Positive Function Renormalization Group (PFRG)... 

Based on extended hydrodynamic calculations and application of the Altenberger-Dahler positive-function renormalization group(12) method, Phillies advanced an entirely different form for jj(c), the stretched exponential(13). 

These properties all indicate that the solutionlike-meltlike transition is mathematical rather than physical in nature. Furthermore, the nature of the positive-function renormalization group is such that a fixed point at the origin naturally yields exponential behavior, while a fixed point away from the origin leads to power-law behavior, precisely as observed for r (c)(9). 

Section II. Because this evolution equation (5.112) also can be derived by requiring the excess function to be positive definite [19], we call this form of the theory the positive (or partition) function renormalization group (PFRG). 

C. J. Boulter, Interface Hamiltonian with a position-dependent stiffness a nonlinear functional renormalization group study, Phys. Rev. E, 57, 2062-2072 (1998). 

With this choice of standard basis functions the 3-F symbols of the group 0 are completely defined from the 34 s3unbols, provided that a positive constant of renormalization is used for each trio of irreducible representations of 0. The trivial 3-F symbols are the even s3nnbols. 

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