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Title: Lattice ϕ 4 field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on S 2

Abstract

We present a method for defining a lattice realization of the Φ 4 quantum field theory on a simplicial complex in order to enable numerical computation on a general Riemann manifold. The procedure begins with adopting methods from traditional Regge calculus (RC) and finite element methods (FEM) plus the addition of ultraviolet counterterms required to reach the renormalized field theory in the continuum limit. The construction is tested numerically for the two-dimensional Φ 4 scalar field theory on the Riemann two-sphere, S 2, in comparison with the exact solutions to the two-dimensional Ising conformal field theory (CFT). Numerical results for the Binder cumulants (up to 12th order) and the two- and four-point correlation functions are in agreement with the exact c = 1 / 2 CFT solutions.

Authors:
; ; ; ; ; ;
Publication Date:
Research Org.:
Brown Univ., Providence, RI (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1459244
Alternate Identifier(s):
OSTI ID: 1498847
Grant/Contract Number:  
SC0015845; SC0014664; SC0010010-Task-A; sc0010010
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 1; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats

Brower, Richard C., Cheng, Michael, Weinberg, Evan S., Fleming, George T., Gasbarro, Andrew D., Raben, Timothy G., and Tan, Chung-I. Lattice ϕ 4 field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on S 2. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.98.014502.
Brower, Richard C., Cheng, Michael, Weinberg, Evan S., Fleming, George T., Gasbarro, Andrew D., Raben, Timothy G., & Tan, Chung-I. Lattice ϕ 4 field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on S 2. United States. doi:10.1103/PhysRevD.98.014502.
Brower, Richard C., Cheng, Michael, Weinberg, Evan S., Fleming, George T., Gasbarro, Andrew D., Raben, Timothy G., and Tan, Chung-I. Fri . "Lattice ϕ 4 field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on S 2". United States. doi:10.1103/PhysRevD.98.014502.
@article{osti_1459244,
title = {Lattice ϕ 4 field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on S 2},
author = {Brower, Richard C. and Cheng, Michael and Weinberg, Evan S. and Fleming, George T. and Gasbarro, Andrew D. and Raben, Timothy G. and Tan, Chung-I},
abstractNote = {We present a method for defining a lattice realization of the Φ4 quantum field theory on a simplicial complex in order to enable numerical computation on a general Riemann manifold. The procedure begins with adopting methods from traditional Regge calculus (RC) and finite element methods (FEM) plus the addition of ultraviolet counterterms required to reach the renormalized field theory in the continuum limit. The construction is tested numerically for the two-dimensional Φ4 scalar field theory on the Riemann two-sphere, S2, in comparison with the exact solutions to the two-dimensional Ising conformal field theory (CFT). Numerical results for the Binder cumulants (up to 12th order) and the two- and four-point correlation functions are in agreement with the exact c = 1 / 2 CFT solutions.},
doi = {10.1103/PhysRevD.98.014502},
journal = {Physical Review D},
number = 1,
volume = 98,
place = {United States},
year = {2018},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevD.98.014502

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Cited by: 2 works
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Works referenced in this record:

Random lattice field theory: General formulation
journal, July 1982


Simplicial Ricci Flow
journal, February 2014

  • Miller, Warner A.; McDonald, Jonathan R.; Alsing, Paul M.
  • Communications in Mathematical Physics, Vol. 329, Issue 2
  • DOI: 10.1007/s00220-014-1911-6

Lattice Dirac fermions on a simplicial Riemannian manifold
journal, June 2017


Over-relaxation methods for Monte Carlo simulations of quadratic and multiquadratic actions
journal, January 1984


Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models
journal, April 2001


Strongly interacting dynamics and the search for new physics at the LHC
journal, June 2016


Conformal invariance and the Ising model on a spheroid
journal, March 2003


Weights of links and plaquettes in a random lattice
journal, October 1982


Lattice radial quantization: 3D Ising
journal, April 2013


General relativity without coordinates
journal, February 1961


Higher-order-magnetization-cumulant universality of the two-dimensional Ising model
journal, January 1997


Calculation of critical exponents in two dimensions from quantum field theory in one dimension
journal, November 1975


Finite element exterior calculus, homological techniques, and applications
journal, May 2006


Dimensional regularisation in the presence of large background fields
journal, September 1982


Collective Monte Carlo Updating for Spin Systems
journal, January 1989


Bulk, surface, and interface properties of the Ising model and conformal invariance
journal, August 1987


Ising universality in three dimensions: a Monte Carlo study
journal, November 1995

  • Blote, H. W. J.; Luijten, E.; Heringa, J. R.
  • Journal of Physics A: Mathematical and General, Vol. 28, Issue 22
  • DOI: 10.1088/0305-4470/28/22/007

General background field calculations with fermion fields
journal, January 1985


Conformal algebra and multipoint correlation functions in 2D statistical models
journal, October 1984


Renormalization of Feynman integrals on the lattice
journal, March 1988

  • Reisz, Thomas
  • Communications in Mathematical Physics, Vol. 117, Issue 1
  • DOI: 10.1007/BF01228412

The connection between the Λ parameters of lattice and continuum QCD
journal, June 1980


Infinite conformal symmetry of critical fluctuations in two dimensions
journal, March 1984

  • Belavin, A. A.; Polyakov, A. M.; Zamolodchikov, A. B.
  • Journal of Statistical Physics, Vol. 34, Issue 5-6
  • DOI: 10.1007/BF01009438

Gauge theory on a random lattice
journal, October 1982


Geometric discretization scheme applied to the Abelian Chern-Simons theory
journal, March 2000


Correlations along a Line in the Two-Dimensional Ising Model
journal, December 1969


Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984


Overrelaxation and Monte Carlo simulation
journal, July 1987


Embedded dynamics for φ 4 theory
journal, March 1989


Erratum: Properties and uses of the Wilson flow in lattice QCD
journal, March 2014


Equation of State Calculations by Fast Computing Machines
journal, June 1953

  • Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N.
  • The Journal of Chemical Physics, Vol. 21, Issue 6
  • DOI: 10.1063/1.1699114

Overrelaxed heat-bath and Metropolis algorithms for accelerating pure gauge Monte Carlo calculations
journal, June 1987


Background field calculations in curved spacetime
journal, April 1984


Properties and uses of the Wilson flow in lattice QCD
journal, August 2010


A power counting theorem for Feynman integrals on the lattice
journal, March 1988

  • Reisz, Thomas
  • Communications in Mathematical Physics, Vol. 116, Issue 1
  • DOI: 10.1007/BF01239027