skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: O( N) and O( N) and O( N)

Abstract

Three related analyses of Φ 4 theory with O( N) symmetry are presented. In the first, we review the O( N) model over the p-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking in an ultrametric context. We demonstrate the existence of a Wilson-Fisher fixed point using an ϵ expansion, and we show how to obtain leading order results for the anomalous dimensions of low dimension operators near the fixed point. Along the way, we note an important aspect of ultrametric field theories, which is a non-renormalization theorem for kinetic terms. In the second analysis, we employ large N methods to establish formulas for anomalous dimensions which are valid equally for field theories over the p-adic numbers and field theories on R n. Results for anomalous dimensions agree between the first and second analyses when they can be meaningfully compared. In the third analysis, we consider higher derivative versions of the O( N) model on R n, the simplest of which has been studied in connection with spatially modulated phases. Our general formula for anomalous dimensions can still be applied. Analogies with two-derivative theories hint at the existence of some interesting unconventional field theoriesmore » in four real Euclidean dimensions.« less

Authors:
 [1];  [1];  [1];  [1]
  1. Princeton Univ., Princeton, NJ (United States). Joseph Henry Lab. of Physics
Publication Date:
Research Org.:
Princeton Univ., NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1507578
Grant/Contract Number:  
FG02-91ER40671
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: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N Expansion; Sigma Models; Renormalization Group

Citation Formats

Gubser, Steven S., Jepsen, Christian, Parikh, Sarthak, and Trundy, Brian. O(N) and O(N) and O(N). United States: N. p., 2017. Web. doi:10.1007/jhep11(2017)107.
Gubser, Steven S., Jepsen, Christian, Parikh, Sarthak, & Trundy, Brian. O(N) and O(N) and O(N). United States. doi:10.1007/jhep11(2017)107.
Gubser, Steven S., Jepsen, Christian, Parikh, Sarthak, and Trundy, Brian. Fri . "O(N) and O(N) and O(N)". United States. doi:10.1007/jhep11(2017)107. https://www.osti.gov/servlets/purl/1507578.
@article{osti_1507578,
title = {O(N) and O(N) and O(N)},
author = {Gubser, Steven S. and Jepsen, Christian and Parikh, Sarthak and Trundy, Brian},
abstractNote = {Three related analyses of Φ4 theory with O(N) symmetry are presented. In the first, we review the O(N) model over the p-adic numbers and the discrete renormalization group transformations which can be understood as spin blocking in an ultrametric context. We demonstrate the existence of a Wilson-Fisher fixed point using an ϵ expansion, and we show how to obtain leading order results for the anomalous dimensions of low dimension operators near the fixed point. Along the way, we note an important aspect of ultrametric field theories, which is a non-renormalization theorem for kinetic terms. In the second analysis, we employ large N methods to establish formulas for anomalous dimensions which are valid equally for field theories over the p-adic numbers and field theories on Rn. Results for anomalous dimensions agree between the first and second analyses when they can be meaningfully compared. In the third analysis, we consider higher derivative versions of the O(N) model on Rn, the simplest of which has been studied in connection with spatially modulated phases. Our general formula for anomalous dimensions can still be applied. Analogies with two-derivative theories hint at the existence of some interesting unconventional field theories in four real Euclidean dimensions.},
doi = {10.1007/jhep11(2017)107},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2017,
place = {United States},
year = {2017},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Phenomenological Discussion of Magnetic Ordering in the Heavy Rare-Earth Metals
journal, October 1961


Conformal invariance in the long-range Ising model
journal, January 2016


Generalized Virasoro models
journal, June 1971

  • Brower, R. C.; Goddard, P.
  • Lettere Al Nuovo Cimento Series 2, Vol. 1, Issue 26
  • DOI: 10.1007/BF02770367

Investigation of the critical point in models of the type of Dyson's hierarchical models
journal, March 1973

  • Bleher, P. M.; Sinai, Ja. G.
  • Communications in Mathematical Physics, Vol. 33, Issue 1
  • DOI: 10.1007/BF01645604

1/n Expansion: Calculation of the exponents ? and? in the order 1/n2 for arbitrary number of dimensions
journal, June 1981

  • Vasil'ev, A. N.; Pis'mak, Yu. M.; Khonkonen, Yu. R.
  • Theoretical and Mathematical Physics, Vol. 47, Issue 3
  • DOI: 10.1007/BF01019296

AdS dual of the critical O(N) vector model
journal, December 2002


Scalar models of p-adic quantum field theory and hierarchical models
journal, February 1989

  • Lerner, �. Yu.; Missarov, M. D.
  • Theoretical and Mathematical Physics, Vol. 78, Issue 2
  • DOI: 10.1007/BF01018683

Critical Exponents for Long-Range Interactions
journal, October 1972


Cayley trees, the Ising problem, and the thermodynamic limit
journal, April 1974


Bootstrapping the O(N) archipelago
journal, November 2015

  • Kos, Filip; Poland, David; Simmons-Duffin, David
  • Journal of High Energy Physics, Vol. 2015, Issue 11
  • DOI: 10.1007/JHEP11(2015)106

Existence of a phase-transition in a one-dimensional Ising ferromagnet
journal, June 1969

  • Dyson, Freeman J.
  • Communications in Mathematical Physics, Vol. 12, Issue 2
  • DOI: 10.1007/BF01645907

The Crossover Region Between Long-Range and Short-Range Interactions for the Critical Exponents
journal, August 2014

  • Brezin, E.; Parisi, G.; Ricci-Tersenghi, F.
  • Journal of Statistical Physics, Vol. 157, Issue 4-5
  • DOI: 10.1007/s10955-014-1081-0

Scaling laws for ising models near T c
journal, June 1966


Renormalization of O ( N ) Nonlinear σ Model on a p -adic Field
journal, October 1988


p-Adic AdS/CFT
journal, January 2017

  • Gubser, Steven S.; Knaute, Johannes; Parikh, Sarthak
  • Communications in Mathematical Physics, Vol. 352, Issue 3
  • DOI: 10.1007/s00220-016-2813-6

Recursion Relations and Fixed Points for Ferromagnets with Long-Range Interactions
journal, July 1973


p-adic numbers in physics
journal, October 1993


Epsilon-expansion in the N-component ϕ 4 model
journal, March 2006


Critical exponents at a Lifshitz point to O(1/n)
journal, December 1975


Ricci curvature of graphs
journal, January 2011

  • Lin, Yong; Lu, Linyuan; Yau, Shing-Tung
  • Tohoku Mathematical Journal, Vol. 63, Issue 4
  • DOI: 10.2748/tmj/1325886283

The analytic structure of conformal blocks and the generalized Wilson-Fisher fixed points
journal, April 2017

  • Gliozzi, Ferdinando; Guerrieri, Andrea L.; Petkou, Anastasios C.
  • Journal of High Energy Physics, Vol. 2017, Issue 4
  • DOI: 10.1007/JHEP04(2017)056

Infinitely Many Commensurate Phases in a Simple Ising Model
journal, June 1980


Renormalization Group and Critical Phenomena. II. Phase-Space Cell Analysis of Critical Behavior
journal, November 1971


Theoretical predictions for critical exponents at the λ-point of bose liquids
journal, October 1971

  • D'eramo, M.; Peliti, L.; Parisi, G.
  • Lettere Al Nuovo Cimento Series 2, Vol. 2, Issue 17
  • DOI: 10.1007/BF02774121

p-adic renormalization group solutions and the euclidean renormalization group conjectures
journal, February 2012


Hyperscaling above the upper critical dimension
journal, December 2012


Critical indices for Dyson's asymptotically-hierarchical models
journal, October 1975

  • Bleher, P. M.; Sinai, Ya. G.
  • Communications in Mathematical Physics, Vol. 45, Issue 3
  • DOI: 10.1007/BF01608331

Phase diagrams near the Lifshitz point. I. Uniaxial magnetization
journal, July 1977


Computation of quark mass anomalous dimension at O(1/Nf2) in quantum chromodynamics
journal, July 2000


Generalized Wilson-Fisher Critical Points from the Conformal Operator Product Expansion
journal, February 2017


Critical Behavior at the Onset of k -Space Instability on the λ Line
journal, December 1975


Edge length dynamics on graphs with applications to p-adic AdS/CFT
journal, June 2017

  • Gubser, Steven S.; Heydeman, Matthew; Jepsen, Christian
  • Journal of High Energy Physics, Vol. 2017, Issue 6
  • DOI: 10.1007/JHEP06(2017)157

The Higgs model with a complex ghost pair
journal, July 1993


The ANNNI model — Theoretical analysis and experimental application
journal, November 1988


A four-dimensional non-linear σ-model
journal, August 1978


Non-archimedean string dynamics
journal, June 1988


Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture
journal, November 1971


Adelic string amplitudes
journal, December 1987


Simple method of calculating the critical indices in the 1/n expansion
journal, February 1981

  • Vasil'ev, A. N.; Pis'mak, Yu. M.; Khonkonen, Yu. R.
  • Theoretical and Mathematical Physics, Vol. 46, Issue 2
  • DOI: 10.1007/BF01030844

Higher spin gauge theory and holography: the three-point functions
journal, September 2010


The renormalization group and the ε expansion
journal, August 1974


New Type of Phase Transition
journal, October 1974


Critical Phenomena and Universal Exponents in Statistical Physics. On Dyson's Hierarchical Model
journal, April 1987


Non-archimedean strings
journal, December 1987