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Physical review. B, Solid state

Critical and tricritical behavior in the hierarchical model

George Allen Baker Jr., Geoffrey R. Golner

Published Sep 1, 1977• 24 citations
Publisher

Abstract

The hierarchical model is solved exactly, numerically in the presence of a magnetic and a staggered magnetic field. Critical and tricritical behavior is studied. The general picture of Riedel and Wegner is confirmed. It is shown that their logarithmic corrections are unobservable owing to the interference of higher-order corrections.
DOI
10.1103/physrevb.16.2081

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Renormalization-group recursion relations are used to calculate to order $\ensuremath{\epsilon}=4\ensuremath{-}d$ the free-energy, ordering-susceptibility, and magnetization-crossover scaling functions for tricritical points in isotropic nnn-vector models. The equations of state describe critical and tricritical behavior in both ordered and disordered phases.