Perturbative analysis of an n-Ising model on a random surface

TL;DR

This paper analyzes a two-dimensional quantum gravity model coupled with matter fields represented by n Ising spins on a random surface, exploring critical behavior and the potential for a well-defined double scaling limit for central charge c>1.

Contribution

It extends previous calculations to higher order and genus, examining the critical properties and double scaling limits of the n-Ising model on random surfaces.

Findings

Calculated string susceptibility exponent at higher orders and genus.

Investigated the existence of a double scaling limit for c>1.

Provided insights into the critical behavior of the model.

Abstract

Two dimensional quantum gravity coupled to a conformally invariant matter field of central charge c=n/2, is represented, in a discretized version, by n independent Ising spins per cell of the triangulations of a random surface. The matrix integral representation of this model leads to a diagrammatic expansion at large orders, when the Ising coupling constant is tuned to criticality, one extracts the values of the string susceptibility exponent. We extend our previous calculation to order eight for genus zero and investigate now also the genus one case in order to check the possibility of having a well-defined double scaling limit even c>1.