Holography for Ising spins on the hyperbolic plane

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.

arXiv comment9 pages, 11 figures

References in corpus (8)

• The Large N Limit of Superconformal Field Theories and Supergravity
• AdS/CFT Correspondence and Symmetry Breaking
• Periodic boundary conditions on the pseudosphere
• Geometric effects on critical behaviours of the Ising model
• Holography on tessellations of hyperbolic space
• Lattice Setup for Quantum Field Theory in AdS${}_2$
• Ising model on hyperbolic lattice studied by corner transfer matrix renormalization group method
• Critical properties of the Ising model in hyperbolic space

Cited by in corpus (3)

• Towards Explicit Discrete Holography: Aperiodic Spin Chains from Hyperbolic Tilings
• Breitenlohner-Freedman bound on hyperbolic tilings
• Aperiodic spin chains at the boundary of hyperbolic tilings