No unitary bootstrap for the fractal Ising model

Golden, John; Paulos, Miguel F.

doi:10.1007/JHEP03(2015)167

Title: No unitary bootstrap for the fractal Ising model

Journal Article · Tue Mar 31 00:00:00 EDT 2015 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/JHEP03(2015)167· OSTI ID:1454588

Golden, John ^[1]; Paulos, Miguel F. ^[2]

Brown Univ., Providence, RI (United States). Dept. of Physics
European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Division

Here, we consider the conformal bootstrap for spacetime dimension 1 < d < 2. We determine bounds on operator dimensions and compare our results with various theoretical and numerical models, in particular with resummed ϵ-expansion and Monte Carlo simulations of the Ising model on fractal lattices. The bounds clearly rule out that these models correspond to unitary conformal field theories. We also clarify the d → 1 limit of the conformal bootstrap, showing that bounds can be — and indeed are — discontinuous in this limit. This discontinuity implies that for small ϵ = d - 1 the expected critical exponents for the Ising model are disallowed, and in particular those of the d - 1 expansion. Altogether these results strongly suggest that the Ising model universality class cannot be described by a unitary CFT below d = 2. We argue this also from a bootstrap perspective, by showing that the 2 ≤ d < 4 Ising “kink” splits into two features which grow apart below d = 2.

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Research Organization:: Brown Univ., Providence, RI (United States); European Organization for Nuclear Research (CERN), Geneva (Switzerland)

Sponsoring Organization:: USDOE Office of Science (SC); European Union (EU)

Grant/Contract Number:: SC0010010; PIEF-GA-2013-623606

OSTI ID:: 1454588

Journal Information:: Journal of High Energy Physics (Online), Vol. 2015, Issue 3; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 18 works

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