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

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.

arXiv comment31 pages, 2 PostScript figures, TeX + epsf.tex

References in corpus (4)

• 2D Gravity and Random Matrices
• $O(N)$ Vector Field Theories in the Double Scaling Limit
• On the Double Scaling Limit of O(N) Vector Models in d=2
• Concerning the Double Scaling Limit in the $O(N)$ Vector Model in Four-Dimensions

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