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

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.

We are grateful to Slava Rychkov for useful discussions and for suggesting this work. The research leading to these results has received funding from the [European Union] Seventh Framework Programme [FP7-People-2010-IRSES] and [FP7/2007-2013] under grant agreements No 269217, 317089 and No 247252, and from the grant CERN/FP/123599/2011. Centro de Física do Porto is partially funded by the Foundation for Science and Technology of Portugal (FCT). J.V.P.L. acknowledges funding from projecto Operacional Regional do Norte, within Quadro de Referência Estratégico Nacional (QREN) and through Fundo Europeu de Desenvolvimento Regional (FEDER), Ref. NORTE-07-0124-FEDER- 000037