The Wilson and functional renormalization group equations

Badis Ydri

Badis Ydri

Claude Bervillier

Eberhard K. Riedel, Kathie E. Newman

Alexander A. Lisyansky, Demetris Nicolaides

A generalized exact renormalization group (RG) equation for the Ginzburg–Landau–Wilson functional of an arbitrary symmetry, containing invariants of all orders, with nonlocal vertices is derived. Unlike other RG equations which contain an infinite number of redundant operators, the equation derived is free of them.

Geoffrey R. Golner, Eberhard K. Riedel

The $\ensuremath{\epsilon}$-expansion formula for the critical exponent $\ensuremath{\eta}$ derived by Shukla and Green from Wilson's exact renormalization-group equation is found to yield the standard result $\ensuremath{\eta}=\frac{1}{54}{\ensuremath{\epsilon}}^{2}+O({\ensuremath{\epsilon}}^{3})$, independent of the choice of the incomplete-integration function. The result is obtained analytically in the limit $a\ensuremath{\rightarrow}\ensuremath{\infty}$ and numerically for arbitrary $a$, where $a$ denotes the normalization constant of the Gaussian fixed-point functional.