Two Ising Models Coupled to 2-Dimensional Gravity

TL;DR

This paper presents large-scale simulations of two coupled Ising models on a dynamical lattice to study their critical behavior and correlations mediated by 2D gravity, highlighting the importance of logarithmic corrections.

Contribution

It provides the first detailed numerical analysis of two Ising models coupled to 2D gravity, including critical exponents and correlation effects.

Findings

Logarithmic corrections are essential for matching theoretical exponents.

Gravity mediates correlations between the two Ising models.

Finite-size scaling reveals critical properties of coupled matter-gravity systems.

Abstract

To investigate the properties of $c=1$ matter coupled to $2$d{--}gravity we have performed large-scale simulations of two copies of the Ising Model on a dynamical lattice. We measure spin susceptibility and percolation critical exponents using finite-size scaling. We show explicitly how logarithmic corrections are needed for a proper comparison with theoretical exponents. We also exhibit correlations, mediated by gravity, between the energy and magnetic properties of the two Ising species. The prospects for extending this work beyond $c=1$ are addressed.