Solutions of the Polchinski ERG equation in the O(N) scalar model

TL;DR

This paper investigates solutions to the Polchinski ERG equation within the O(N) scalar model, identifying families of solutions and their connection to fixed points, especially analyzing the large N limit analytically.

Contribution

It provides new analytical and numerical solutions to the Polchinski ERG equation in the O(N) model, clarifying their relation to fixed points and exploring the large N limit.

Findings

Families of regular solutions are identified.

The relation between solutions and fixed points is established.

Analytical insights are gained in the N=∞ limit.

Abstract

Solutions of the Polchinski exact renormalization group equation in the scalar O(N) theory are studied. Families of regular solutions are found and their relation with fixed points of the theory is established. Special attention is devoted to the limit $N=\infty$, where many properties can be analyzed analytically.