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)]}.

References in corpus (10)

• Solving the 3D Ising Model with the Conformal Bootstrap
• Precision Islands in the Ising and $O(N)$ Models
• The Lightcone Bootstrap and the Spectrum of the 3d Ising CFT
• The Magnetization of the 3D Ising Model
• TASI Lectures on the Conformal Bootstrap
• Thermodynamic Casimir effect: Universality and Corrections to Scaling
• Numerical determination of OPE coefficients in the 3D Ising model from off-critical correlators
• OPE Coefficients of the 3D Ising model with a trapping potential
• A Monte Carlo method for critical systems in infinite volume: the planar Ising model
• Markov chain sampling of the $O(n)$ loop models on the infinite plane

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• Energy trapped Ising model
• The Operator Product Expansion for Radial Lattice Quantization of 3D ${\varphi }^4$ Theory