High-accuracy scaling exponents in the local potential approximation

Bervillier, Claude; Juttner, Andreas; Litim, Daniel F.

High-accuracy scaling exponents in the local potential approximation

Authors

Bervillier, Claude

Juttner, Andreas

Litim, Daniel F.

Description

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.
9 pages, 7 figures, comparison and discussion/conclusions sharpened, references added