High-accuracy scaling exponents in the local potential approximation. (English) Zbl 1150.82002
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.
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 82B28 | Renormalization group methods in equilibrium statistical mechanics |
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