Conformal symmetry of the critical 3D Ising model inside a sphere

TL;DR

This study uses Monte-Carlo simulations to investigate the conformal symmetry of the critical 3D Ising model within a spherical boundary, providing numerical evidence supporting theoretical predictions.

Contribution

First numerical verification of conformal symmetry predictions for the 3D Ising model inside a sphere using Monte-Carlo methods.

Findings

Results align with conformal symmetry predictions

One and two point functions match theoretical expectations

Supports the conjecture of conformal invariance at criticality

Abstract

We perform Monte-Carlo simulations of the three-dimensional Ising model at the critical temperature and zero magnetic field. We simulate the system in a ball with free boundary conditions on the two dimensional spherical boundary. Our results for one and two point functions in this geometry are consistent with the predictions from the conjectured conformal symmetry of the critical Ising model.