Dynamical Selection of Critical Exponents

Abstract

In renormalized field theories there are in general one or few fixed points which are accessible by the renormalization-group flow. They can be identified from the fixed-point equations. Exceptionally, an infinite family of fixed points exists, parameterized by a scaling exponent $\zeta$, itself function of a non-renormalizing parameter. Here we report a different scenario with an infinite family of fixed points of which seemingly only one is chosen by the renormalization-group flow. This dynamical selection takes place in systems with an attractive interaction $\mathcal{V}(\varphi )$, as in standard ${\varphi }^4$ theory, but where the potential $\mathcal{V}$ at large $\varphi$ goes to zero, as e.g. the attraction by a defect.

v2: Several misprints corrected, appendix on toy model rendered more relevant. 13 pages, 22 figures

References in corpus (2)

• Height fluctuations of a contact line: a direct measurement of the renormalized disorder correlator
• Numerical Calculation of the Functional renormalization group fixed-point functions at the depinning transition

Cited by in corpus (3)

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• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• Theory and Experiments for Disordered Elastic Manifolds, Depinning, Avalanches, and Sandpiles