O(N) models within the local potential approximation

TL;DR

This paper investigates the critical properties of O(N) vector models using the Wegner-Houghton equation within the Local Potential Approximation, analyzing fixed points, critical exponents, and eigenoperators for various N, including special cases like N=0 and N→∞.

Contribution

It provides a comprehensive analysis of O(N) models' critical behavior using the Wegner-Houghton and Polchinski equations, including the large N limit and special cases.

Findings

Fixed points and critical exponents for various N

Line of fixed points at d=2+2/n for large N

Detailed study of large N limit peculiarities

Abstract

Using Wegner-Houghton equation, within the Local Potential Approximation, we study critical properties of O(N) vector models. Fixed Points, together with their critical exponents and eigenoperators, are obtained for a large set of values of N, including N=0 and N\to\infty. Polchinski equation is also treated. The peculiarities of the large N limit, where a line of Fixed Points at d=2+2/n is present, are studied in detail. A derivation of the equation is presented together with its projection to zero modes.