O(N)-invariant Hierarchical Renormalization Group Fixed Points by Algebraic Numerical Computation and ε-Expansion

Details O(N)-invariant Hierarchical Renormalization Group Fixed Points by Algebraic Numerical Computation and ε-Expansion O(N)-invariant Hierarchical Renormalization Group Fixed Points by Algebraic Numerical Computation and ε-Expansion

1999-09-29

arxiv.org/abs/cond-mat/9909418v2

Physics

Condensed Matter

Statistical Mechanics

30 pages, 9 figures; changed 2 figures for better printing, completed list of references, changed font to 11pt, submitted to J

Scientific paper

Generalizing methods developed by Pinn, Pordt and Wieczerkowski for the hierarchical model with one component (N=1) and dimensions d between 2 and 4 we compute O(N)-symmetric fixed points of the hierarchical renormalization group equation for some N and d with 0 < d < 4 and -2 <= N <= 20. The spectra of the linearized RG equation at the fixed points are calculated and the critical exponents \nu are extracted from the spectrum and compared to Borel-Pade-resummed \epsilon-expansion.

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