Geodesic
Attractor properties of physical branches of the solution to the renormalization group equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 117 (1998) no. 3, pp. 397-410 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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A. E. Filippov. Attractor properties of physical branches of the solution to the renormalization group equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 117 (1998) no. 3, pp. 397-410. http://geodesic.mathdoc.fr/item/TMF_1998_117_3_a5/

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