High-accuracy scaling exponents in the local potential approximation

We test equivalences between different realisations of Wilson's renormalisation group by computing the leading, subleading, and anti-symmetric corrections-to-scaling exponents, and the full fixed point potential for the Ising universality class to leading order in a derivative expansion. We dis...

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Bibliographic Details
Published in:Nuclear physics. B 2007-11, Vol.783 (3), p.213-226
Main Authors: Bervillier, Claude, Jüttner, Andreas, Litim, Daniel F.
Format: Article
Language:English
Subjects:
Condensed Matter
High Energy Physics - Phenomenology
High Energy Physics - Theory
Physics
Statistical Mechanics
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Summary:We test equivalences between different realisations of Wilson's renormalisation group by computing the leading, subleading, and anti-symmetric corrections-to-scaling exponents, and the full fixed point potential for the Ising universality class to leading order in a derivative expansion. We discuss our methods with a special emphasis on accuracy and reliability. We establish numerical equivalence of Wilson–Polchinski flows and optimised renormalisation group flows with an unprecedented accuracy in the scaling exponents. Our results are contrasted with high-accuracy findings from Dyson's hierarchical model, where a tiny but systematic difference in all scaling exponents is established. Further applications for our numerical methods are briefly indicated.
ISSN:0550-3213
1873-1562
DOI:10.1016/j.nuclphysb.2007.03.036