Double Scaling Limits, Airy Functions and Multicritical Behaviour in O(N) Vektor Sigma Models

TL;DR

This paper explores the behavior of O(N) vector sigma models with critical points, revealing that their partition functions exhibit generalized Airy functions or scalar field theory partition functions under specific large-N and coupling scalings.

Contribution

It introduces a novel analysis of the double scaling limit in O(N) sigma models, connecting critical phenomena to Airy functions and scalar field theories.

Findings

Partition functions develop singular factors in the double scaling limit.

Generalized Airy functions emerge in zero-dimensional models.

Scalar field theory partition functions appear in positive dimensions.

Abstract

O(N) vector sigma models possessing catastrophes in their action are studied. Coupling the limit N --> infinity with an appropriate scaling behaviour of the coupling constants, the partition function develops a singular factor. This is a generalized Airy function in the case of spacetime dimension zero and the partition function of a scalar field theory for positive spacetime dimension.