Double Scaling Limits and Catastrophes of the zerodimensional O(N) Vector Sigma Model: The A-Series

TL;DR

This paper investigates the behavior of the zerodimensional O(N) vector sigma model near critical points, using saddle point methods and generalized Airy functions to analyze partition function catastrophes.

Contribution

It introduces a novel saddle point analysis approach for the model's partition functions near catastrophes, linking them to generalized Airy functions.

Findings

Partition functions expressed via generalized Airy functions.

Identification of critical phenomena and phase transitions.

Analytical characterization of model behavior near catastrophes.

Abstract

We evaluate the partition functions in the neighbourhood of catastrophes by saddle point integration and express them in terms of generalized Airy functions.