No unitary bootstrap for the fractal Ising model
Abstract
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.
- Authors:
-
- Brown Univ., Providence, RI (United States). Dept. of Physics
- European Organization for Nuclear Research (CERN), Geneva (Switzerland). Theory Division
- Publication Date:
- Research Org.:
- Brown Univ., Providence, RI (United States); European Organization for Nuclear Research (CERN), Geneva (Switzerland)
- Sponsoring Org.:
- USDOE Office of Science (SC); European Union (EU)
- OSTI Identifier:
- 1454588
- Grant/Contract Number:
- SC0010010; PIEF-GA-2013-623606
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of High Energy Physics (Online)
- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 3; Journal ID: ISSN 1029-8479
- Publisher:
- Springer Berlin
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Field Theories in Lower Dimensions; Nonperturbative Effects
Citation Formats
Golden, John, and Paulos, Miguel F. No unitary bootstrap for the fractal Ising model. United States: N. p., 2015.
Web. doi:10.1007/JHEP03(2015)167.
Golden, John, & Paulos, Miguel F. No unitary bootstrap for the fractal Ising model. United States. https://doi.org/10.1007/JHEP03(2015)167
Golden, John, and Paulos, Miguel F. Tue .
"No unitary bootstrap for the fractal Ising model". United States. https://doi.org/10.1007/JHEP03(2015)167. https://www.osti.gov/servlets/purl/1454588.
@article{osti_1454588,
title = {No unitary bootstrap for the fractal Ising model},
author = {Golden, John and Paulos, Miguel F.},
abstractNote = {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.},
doi = {10.1007/JHEP03(2015)167},
journal = {Journal of High Energy Physics (Online)},
number = 3,
volume = 2015,
place = {United States},
year = {Tue Mar 31 00:00:00 EDT 2015},
month = {Tue Mar 31 00:00:00 EDT 2015}
}
Web of Science
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