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

## TL;DR

This paper extends the UV sampler method to the 3d Ising model, enabling numerical estimation of key conformal field theory data such as structure constants and scaling weights, aligning well with bootstrap results.

## Contribution

It generalizes the UV sampler technique from 2D to 3D, providing a new numerical approach for estimating CFT data in higher dimensions.

## Key findings

- Accurate estimation of structure constants in 3D Ising CFT.
- Results agree with recent bootstrap estimates.
- Demonstrates the effectiveness of the generalized 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)]}.