# Spin-spin correlation functions of spin systems coupled to 2-d quantum gravity for $0 < c < 1$

## TL;DR

This paper uses Monte Carlo simulations to study spin systems coupled to 2D quantum gravity, revealing diverging correlation lengths at critical points and confirming theoretical KPZ predictions.

## Contribution

It provides numerical evidence linking spin-spin correlation functions to KPZ exponents in 2D quantum gravity coupled matter models.

## Key findings

- Diverging correlation length at critical temperature.
- Correlation functions match KPZ scaling exponents.
- Supports theoretical conjectures on matter-gravity coupling.

## Abstract

We perform Monte Carlo simulations of 2-d dynamically triangulated surfaces coupled to Ising and three--states Potts model matter. By measuring spin-spin correlation functions as a function of the geodesic distance we provide substantial evidence for a diverging correlation length at $\beta_c$. The corresponding scaling exponents are directly related to the KPZ exponents of the matter fields as conjectured in [4] (NPB454(1995)313).