Dynamical selection of critical exponents.

Abstract

In renormalized field theories there are in general one or few fixed points that 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 ζ, itself a function of a nonrenormalizing 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 V(ϕ), as in standard ϕ^{4} theory, but where the potential V at large ϕ goes to zero, as, e.g., the attraction by a defect.