O(N)-invariant Hierarchical Renormalization Group Fixed Points by Algebraic Numerical Computation and \epsilon-Expansion
Statistical Mechanics
2007-05-23 v2 High Energy Physics - Theory
Abstract
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.
Cite
@article{arxiv.cond-mat/9909418,
title = {O(N)-invariant Hierarchical Renormalization Group Fixed Points by Algebraic Numerical Computation and \epsilon-Expansion},
author = {J. Goettker-Schnetmann},
journal= {arXiv preprint arXiv:cond-mat/9909418},
year = {2007}
}
Comments
30 pages, 9 figures; changed 2 figures for better printing, completed list of references, changed font to 11pt, submitted to Journal of Statistical Physics