Polchinski ERG Equation in O(N) Scalar Field Theory

Abstract

We investigate the Polchinski ERG equation for d-dimensional O(N) scalar field theory. In the context of the non-perturbative derivative expansion we find families of regular solutions and establish their relation with the physical fixed points of the theory. Special emphasis is given to the large N limit for which many properties can be studied analytically.

7 pages, 4 figures, uses latex sprocl style. Two references added. To be published in the proceedings of the Second Conference on the Exact Renormalization Group (Rome, September 18-22, 2000), World Scientific

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• Why Might the Standard Large $N$ Analysis Fail in the O($N$) Model: The Role of Cusps in the Fixed Point Potentials
• Revisiting the local potential approximation of the exact renormalization group equation
• Solutions of the Polchinski ERG equation in the O(N) scalar model
• Incompleteness of the large-$N$ analysis of the $O(N)$ models: Nonperturbative cuspy fixed points and their nontrivial homotopy at finite $N$
• A fixed point can hide another one: the nonperturbative behavior of the tetracritical fixed point of the O($N$) models at large $N$