An approximation for random surfaces on arbitrary target spaces

TL;DR

This paper develops a perturbative low-temperature expansion technique for matrix models of random surfaces applicable to arbitrary target spaces, providing accurate estimates for critical exponents across different regimes.

Contribution

It introduces a novel perturbative method for analyzing random surfaces with diverse target spaces, including those with c>1, and demonstrates its effectiveness through detailed calculations.

Findings

Series expanded to 10th order for q-state Potts model

Accurate estimates for critical exponent gamma_str

Logarithmic corrections to scaling identified

Abstract

A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked out to 10th order for the surface coupled to a q-state Potts model. Accurate estimates for, e.g., $\gamma_{str}$ are obtained both in the low q (c<1) and high q (branched polymer) regimes, including the logarithmic corrections to scaling.