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

Abstract

With a view to study the convergence properties of the derivative expansion of the exactrenormalization group (RG) equation, I explicitly study the leading and next-to-leadingorders of this expansion applied to the Wilson–Polchinski equation in the case of theN-vector model with thesymmetry O (N). As a test,the critical exponents η and ν as well as thesubcritical exponent ω (and higher ones) are estimated in three dimensions for values ofN rangingfrom 1 to 20. Icompare the results with the corresponding estimates obtained in preceding studies or treatments ofother O (N) exact RG equations at second order. The possibility of varyingN allows the derivative expansion method to be better valued. The values obtained from theresummation of high orders of perturbative field theory are used as standards to illustratethe eventual convergence in each case. Particular attention is drawn to the preservation (ornot) of the reparameterization invariance.