Critical Ising Model in Varying Dimension by Conformal Bootstrap

Abstract

The single-correlator conformal bootstrap is solved numerically for several values of dimension 4>d>2 using the available SDPB and Extremal Functional methods. Critical exponents and other conformal data of low-lying states are obtained over the entire range of dimensions with up to four-decimal precision and then compared with several existing results. The conformal dimensions of leading-twist fields are also determined up to high spin, and their d-dependence shows how the conformal states rearrange themselves around d=2.2 for matching the Virasoro conformal blocks in the d=2 limit. The decoupling of states at the Ising point is studied for 3>d>2 and the vanishing of one structure constant at d=3 is found to persist till d=2 where it corresponds to a Virasoro null-vector condition.

arXiv comment43 pages, 15 figures, 7 tables, numerical data and Mathematica files are available upon request; v2: epsilon-expansion data added

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• New Developments in the Numerical Conformal Bootstrap
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• Complex networks with tuneable dimensions as a universality playground
• Simple non-perturbative resummation schemes beyond mean-field: case study for scalar ${\varphi }^4$ theory in 1+1 dimensions
• Spectrum continuity and level repulsion: the Ising CFT from infinitesimal to finite $\mathbf{\epsilon }$
• Perturbative and Nonperturbative Studies of CFTs with MN Global Symmetry
• Ising model close to $d=2$
• Navigating through the O(N) archipelago
• The tricritical Ising CFT and conformal bootstrap
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• Stability of ${\phi }^4$-vector model: four-loop $\epsilon$ expansion study
• Operator product expansion coefficients from the nonperturbative functional renormalization group
• On the Wilson-Fisher fixed point in the limit of integer spacetime dimensions