Grand-Canonical Ensemble of Random Surfaces with Four Species of Ising Spins

TL;DR

This paper simulates a grand-canonical ensemble of random surfaces with four Ising spin species, analyzing the string susceptibility exponent and proposing a conjecture for models with central charge greater than one.

Contribution

It introduces a computational simulation of coupled random surfaces and Ising spins with new insights into the string susceptibility exponent for c=2 models.

Findings

Effective string susceptibility exponent γ ≈ -0.195

Simulation of surfaces with up to 1000 vertices

Conjecture for behavior of models with c > 1

Abstract

The grand-canonical ensemble of dynamically triangulated surfaces coupled to four species of Ising spins (c=2) is simulated on a computer. The effective string susceptibility exponent for lattices with up to 1000 vertices is found to be $\gamma = - 0.195(58)$. A specific scenario for $c > 1$ models is conjectured.