Holography for Ising spins on the hyperbolic plane

Muhammad Asaduzzaman, Simon Catterall, Jay Hubisz, Roice Nelson, Judah Unmuth-Yockey

Research output: Contribution to journalArticlepeer-review

Abstract

Motivated by the AdS/CFT correspondence, we use Monte Carlo simulation to investigate the Ising model formulated on tessellations of the two-dimensional hyperbolic disk. We focus in particular on the behavior of boundary-boundary correlators, which exhibit power-law scaling both below and above the bulk critical temperature indicating scale invariance of the boundary theory at any temperature. This conclusion is strengthened by a finite-size scaling analysis of the boundary susceptibility which yields a scaling exponent consistent with the scaling dimension extracted from the boundary correlation function. This observation provides evidence that the connection between continuum boundary conformal symmetry and isometries of the bulk hyperbolic space survives for simple interacting field theories even when the bulk is approximated by a discrete tessellation.

Original languageEnglish (US)
Article number054506
JournalPhysical Review D
Volume106
Issue number5
DOIs
StatePublished - Sep 1 2022

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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