Journal article

ANALOGS OF RENORMALIZATION-GROUP TRANSFORMATIONS IN RANDOM-PROCESSES

MF SHLESINGER, BD HUGHES

PHYSICA A | ELSEVIER SCIENCE BV | Published : 1981

Abstract

We review the properties of a real-space renormalization group transformation of the free energy, including the existence of oscillatory terms multiplying the non-analytic part of the free energy. We then construct stochastic processes which incorporate into probability distributions the features of the free energy scaling equation. (The essential information is obtainable from the scaling equation and a direct solution for a probability is not necessary.) These random processes are shown to be generated directly from Cantor sets. In a spatial representation, the ensuing random process exhibits a transition between Gaussian and fractal behavior. In the fractal regime, the trajectories will, ..

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University of Melbourne Researchers