This article is cited in 1 paper

Attractor properties of physical branches of the solution to the renormalization group equation

A. E. Filippov

Donetsk Physical-Technical Institute, National Academy of Sciences of Ukraine

Abstract: We investigate the global phase-portrait structure of a local version of the exact renormalization group (RG) equation for a fluctuating scalar field of the order parameter. All the physical branches of the RG equation solution for the fixed points belong to the attractor subspace to which the local density of the Ginzburg–Landau–Wilson functional is attracted for largely arbitrary initial configurations. The solution of the RG equation corresponding to the nontrivial fixed point determining the critical behavior under the second-order phase transition is a fixed saddle point of this attractor subspace separating the attraction domains of two stable solutions corresponding to the high- and low-temperature thermodynamic regimes.

Received: 18.09.1997
Revised: 17.07.1998

DOI: 10.4213/tmf941

 English version: Theoretical and Mathematical Physics, 1998, 117:3, 1423–1433

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