Wilson-Polchinski exact renormalization group equation for O(N) systems: leading and next-to-leading orders in the derivative expansion

摘要

With a view to study the convergence properties of the derivative expansion of the exact renormalization group (RG) equation, I explicitly study the leading and next-to-leading orders of this expansion applied to the Wilson-Polchinski equation in the case of the N-vector model with the symmetry O(N). As a test, the critical exponents eta and v as well as the subcritical exponent omega (and higher ones) are estimated in three dimensions for values of N ranging from 1 to 20. I compare the results with the corresponding estimates obtained in preceding studies or treatments of other O(N) exact RG equations at second order. The possibility of varying N allows the derivative expansion method to be better valued. The values obtained from the resummation of high orders of perturbative field theory are used as standards to illustrate the eventual convergence in each case. Particular attention is drawn to the preservation (or not) of the reparameterization invariance.