Ising Spins on a Gravitating Sphere

TL;DR

This study numerically examines the Ising model on a spherical gravitational background, confirming that its critical behavior aligns with flat-space universality class and excludes KPZ predictions.

Contribution

It provides evidence that the Ising model on a spherical gravitational surface exhibits Onsager universality, extending previous toroidal topology results.

Findings

Critical exponents match Onsager values.

KPZ exponents are excluded.

Spherical topology does not alter universality class.

Abstract

We investigated numerically an Ising model coupled to two-dimensional Euclidean gravity with spherical topology, using Regge calculus with the $dl/l$ path-integral measure to discretize the gravitational interaction. Previous studies of this system with toroidal topology have shown that the critical behavior of the Ising model remains in the flat-space Onsager universality class, contrary to the predictions of conformal field theory and matrix models. Implementing the spherical topology as triangulated surfaces of three-dimensional cubes, we find again strong evidence that the critical exponents of the Ising transition are consistent with the Onsager values, and that KPZ exponents are definitely excluded.