# 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.

## Key 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.

---
Source: https://tomesphere.com/paper/hep-lat/9512002