Solutions of matrix models in the DIII generator ensemble

TL;DR

This paper solves two matrix models within the DIII generator ensemble, revealing their free energy behavior in the double scaling limit and discovering an additional solution for one model.

Contribution

It introduces new techniques to solve antisymmetric matrix models in the DIII ensemble and identifies an extra solution for one of the models.

Findings

Free energy exhibits similar behavior to known models in the double scaling limit

An additional solution was found for the first matrix model

Models describe oriented and unoriented surfaces

Abstract

In this paper we solve two matrix models, using standard and new techniques. The two models are represented by special form of antisymmetric matrices and are classified in the DIII generator ensemble. It is shown that, in the double scaling limit, their free energy has the same behavior as previous models describing oriented and unoriented surfaces. We also found an additional solution for the first model.