The O(N) vector model in the large N limit revisited: multicritical points and double scaling limit

TL;DR

This paper revisits the large N limit of the O(N) vector model, focusing on multicritical points, phase stability, and the double scaling limit, revealing conditions for non-interacting singlet fields at critical dimensions.

Contribution

It provides a detailed analysis of the multicritical points and the double scaling limit in the O(N) vector model, highlighting new insights into phase stability and singlet bound states.

Findings

Massless singlet bound state forms in the double scaling limit.

Double scaled theory can be non-interacting at critical dimensions.

Persistence of large N results beyond leading order examined.

Abstract

The multicritical points of the $O(N)$ invariant $N$ vector model in the large $N$ limit are reexamined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit $N \to \infty$ while the coupling $g \to g_c$ in a correlated manner (the double scaling limit) a massless bound state $O(N)$ singlet is formed and powers of $1/N$ are compensated by IR singularities. The persistence of the $N \to \infty$ results beyond the leading order is then studied with particular interest in the possible existence of a phase with propagating small mass vector fields and a massless singlet bound state. We point out that under certain conditions the double scaled theory of the singlet field is non-interacting in critical dimensions.