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Numerical estimation of structure constants in the three-dimensional Ising conformal field theory through Markov
1Department of Mathematics, King's College, London WC2R 2LS, United Kingdom.
Abstract:
Herdeiro and Doyon [Phys. Rev. E 94, 043322 (2016)2470-004510.1103/PhysRevE.94.043322] introduced a numerical recipe, dubbed uv sampler, offering precise estimations of the conformal field theory (CFT) data of the planar two-dimensional (2D) 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 Monte Carlo sampler is the invariance under dilation. This paper 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 [Kos, Poland, Simmons-Duffin, and Vichi, J. High Energy Phys. 08 (2016) 03610.1007/JHEP08(2016)036].
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