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Solving the 3d Ising Model with the Conformal Bootstrap II. c c -Minimization and Precise Critical Exponents

2014/03/31 by Sheer El-Showk, Miguel F. Paulos, David Poland +4 · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Central charge #Combinatorics #Conformal field theory #Conformal map #Conjecture #Degenerate energy levels #Dimension (graph theory) #Geometry #Ising model #Mathematical analysis #Mathematical physics #Mathematics #Operator (biology) #Physics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Random Matrices and Applications #Spectrum (functional analysis) #Statistical physics #Symmetry (geometry) #cond-mat.stat-mech #cond-mat.str-el #hep-lat #hep-th #math-ph #math.MP

paper · pdf · doi:10.1007/s10955-014-1042-7

published as J. Stat. Phys. 157, 869-914 (2014) · 55 pages, many figures; v2 - refs and comments added, to appear in a special issue of J.Stat.Phys. in memory of Kenneth Wilson

arxiv created 2014/06/04 · openalex publication_date 2014/06/25 · arxiv updated 2014/12/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We use the conformal bootstrap to perform a precision study of the operator spectrum of the critical 3d Ising model. We conjecture that the 3d Ising spectrum minimizes the central charge c in the space of unitary solutions to crossing symmetry. Because extremal solutions to crossing symmetry are uniquely determined, we are able to precisely reconstruct the first several Z2-even operator dimensions and their OPE coefficients. We observe that a sharp transition in the operator spectrum occurs at the 3d Ising dimension Deltasigma=0.518154(15), and find strong numerical evidence that operators decouple from the spectrum as one approaches the 3d Ising point. We compare this behavior to the analogous situation in 2d, where the disappearance of operators can be understood in terms of degenerate Virasoro representations.

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