Renormalization group as a Koopman operator.
basic_science · Level V
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- Record sourced from PubMed, PMID 32688576.
- Also identified by DOI 10.1103/PhysRevE.101.060104.
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Abstract
Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents η and δ, as well as ratios of critical exponents, of classical spin systems from single observables alone. This broadens the types of problems that the renormalization group framework can be applied to and establish universality classes of. In addition, this connection may allow for a new, data-driven way in which to find the renormalization group fixed point(s), and their relevant and irrelevant directions.