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

Catarina Cosme,J M Viana Parente Lopes,João Penedones

doi:10.1007/jhep08(2015)022

Catarina Cosme, J M Viana Parente Lopes + Show 1 more

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https://doi.org/10.1007/jhep08(2015)022

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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.

Highlights

JHEP08(2015)022 where the local spin variables can take two values s(x) = ±1 and the sum is over nearest neighbours in a cubic lattice
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
The local operators in the Ising model can be classified by their quantum numbers with respect to the Z2 spin-flip symmetry and the point group symmetry of the cubic lattice

Summary

Introduction

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 interested in correlation functions of local operators at the critical temperature The local lattice operators can be written in terms of the operators of the Ising CFT that have the same symmetry properties. We normalize the CFT operators imposing the following correlation functions in the infinite system without boundaries

Results

Conclusion