Numerical estimation of structure constants in the 3d Ising CFT through Markov chain UV sampler

Abstract

[Herdeiro & Doyon Phys., Rev., E (2016)] https://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.043322 introduced a numerical recipe, dubbed UV sampler, offering precise estimations of the CFT data of the planar two-dimensional critical Ising model. It made use of scale invariance emerging at the critical point in order to sample finite sublattice marginals of the infinite plane Gibbs measure of the model by producing ``holographic" boundary distributions. The main ingredient of the Markov chain MonteCarlo (MCMC) sampler is the invariance under dilation. This article presents a generalization to higher dimensions with the critical 3d Ising model. This leads to numerical estimations of a subset of the CFT data - scaling weights and structure constants - through fitting of measured correlation functions. The results are shown to agree with the recent most precise estimations from numerical bootstrap methods \href{https://arxiv.org/abs/1603.04436}{[Kos,\;Poland,\;Vicci\;\&\;Simmons-Duffin JHEP (2016)]}.