Lattice field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on
Abstract
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 counter terms 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, $$\mathbb{s}$$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); Boston Univ., MA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1459244
- Alternate Identifier(s):
- OSTI ID: 1498847; OSTI ID: 1833391
- 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. https://doi.org/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. https://doi.org/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 counter terms 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, $\mathbb{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.},
doi = {10.1103/PhysRevD.98.014502},
journal = {Physical Review D},
number = 1,
volume = 98,
place = {United States},
year = {2018},
month = {7}
}
https://doi.org/10.1103/PhysRevD.98.014502
Web of Science
Works referenced in this record:
Random lattice field theory: General formulation
journal, July 1982
- Christ, N. H.; Friedberg, R.; Lee, T. D.
- Nuclear Physics B, Vol. 202, Issue 1
Simplicial Ricci Flow
journal, February 2014
- Miller, Warner A.; McDonald, Jonathan R.; Alsing, Paul M.
- Communications in Mathematical Physics, Vol. 329, Issue 2
Lattice Dirac fermions on a simplicial Riemannian manifold
journal, June 2017
- Brower, Richard C.; Weinberg, Evan S.; Fleming, George T.
- Physical Review D, Vol. 95, Issue 11
Over-relaxation methods for Monte Carlo simulations of quadratic and multiquadratic actions
journal, January 1984
- Whitmer, Charles
- Physical Review D, Vol. 29, Issue 2
Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models
journal, April 2001
- Binder, Kurt; Luijten, Erik
- Physics Reports, Vol. 344, Issue 4-6
Strongly interacting dynamics and the search for new physics at the LHC
journal, June 2016
- Appelquist, T.; Brower, R. C.; Fleming, G. T.
- Physical Review D, Vol. 93, Issue 11
Conformal invariance and the Ising model on a spheroid
journal, March 2003
- Deng, Youjin; Blöte, Henk W. J.
- Physical Review E, Vol. 67, Issue 3
Weights of links and plaquettes in a random lattice
journal, October 1982
- Christ, N. H.; Friedberg, R.; Lee, T. D.
- Nuclear Physics B, Vol. 210, Issue 3
Lattice radial quantization: 3D Ising
journal, April 2013
- Brower, R. C.; Fleming, G. T.; Neuberger, H.
- Physics Letters B, Vol. 721, Issue 4-5
General relativity without coordinates
journal, February 1961
- Regge, T.
- Il Nuovo Cimento, Vol. 19, Issue 3
Higher-order-magnetization-cumulant universality of the two-dimensional Ising model
journal, January 1997
- Mon, K. K.
- Physical Review B, Vol. 55, Issue 1
Calculation of critical exponents in two dimensions from quantum field theory in one dimension
journal, November 1975
- Luther, A.; Peschel, I.
- Physical Review B, Vol. 12, Issue 9
Finite element exterior calculus, homological techniques, and applications
journal, May 2006
- Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
- Acta Numerica, Vol. 15
Dimensional regularisation in the presence of large background fields
journal, September 1982
- Lüscher, M.
- Annals of Physics, Vol. 142, Issue 2
Collective Monte Carlo Updating for Spin Systems
journal, January 1989
- Wolff, Ulli
- Physical Review Letters, Vol. 62, Issue 4
Bulk, surface, and interface properties of the Ising model and conformal invariance
journal, August 1987
- Burkhardt, Theodore W.; Guim, Ihnsouk
- Physical Review B, Vol. 36, Issue 4
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
General background field calculations with fermion fields
journal, January 1985
- Jack, I.; Osborn, H.
- Nuclear Physics B, Vol. 249, Issue 3
Conformal algebra and multipoint correlation functions in 2D statistical models
journal, October 1984
- Dotsenko, Vl. S.; Fateev, V. A.
- Nuclear Physics B, Vol. 240, Issue 3
Renormalization of Feynman integrals on the lattice
journal, March 1988
- Reisz, Thomas
- Communications in Mathematical Physics, Vol. 117, Issue 1
The connection between the Λ parameters of lattice and continuum QCD
journal, June 1980
- Hasenfratz, Anna; Hasenfratz, Peter
- Physics Letters B, Vol. 93, Issue 1-2
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
Gauge theory on a random lattice
journal, October 1982
- Christ, N. H.; Friedberg, R.; Lee, T. D.
- Nuclear Physics B, Vol. 210, Issue 3
Geometric discretization scheme applied to the Abelian Chern-Simons theory
journal, March 2000
- Sen, Samik; Sen, Siddhartha; Sexton, James C.
- Physical Review E, Vol. 61, Issue 3
Correlations along a Line in the Two-Dimensional Ising Model
journal, December 1969
- Kadanoff, Leo P.
- Physical Review, Vol. 188, Issue 2
Infinite conformal symmetry in two-dimensional quantum field theory
journal, July 1984
- Belavin, A. A.; Polyakov, A. M.; Zamolodchikov, A. B.
- Nuclear Physics B, Vol. 241, Issue 2
Overrelaxation and Monte Carlo simulation
journal, July 1987
- Creutz, Michael
- Physical Review D, Vol. 36, Issue 2
Embedded dynamics for theory
journal, March 1989
- Brower, Richard C.; Tamayo, Pablo
- Physical Review Letters, Vol. 62, Issue 10
Erratum: Properties and uses of the Wilson flow in lattice QCD
journal, March 2014
- Lüscher, Martin
- Journal of High Energy Physics, Vol. 2014, Issue 3
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
Overrelaxed heat-bath and Metropolis algorithms for accelerating pure gauge Monte Carlo calculations
journal, June 1987
- Brown, Frank R.; Woch, Thomas J.
- Physical Review Letters, Vol. 58, Issue 23
Background field calculations in curved spacetime
journal, April 1984
- Jack, I.; Osborn, H.
- Nuclear Physics B, Vol. 234, Issue 2
Properties and uses of the Wilson flow in lattice QCD
journal, August 2010
- Lüscher, Martin
- Journal of High Energy Physics, Vol. 2010, Issue 8
A power counting theorem for Feynman integrals on the lattice
journal, March 1988
- Reisz, Thomas
- Communications in Mathematical Physics, Vol. 116, Issue 1
Over-relaxation method for the Monte Carlo evaluation of the partition function for multiquadratic actions
journal, June 1981
- Adler, Stephen L.
- Physical Review D, Vol. 23, Issue 12
Nouvelles applications des paramètres continus à la théorie des formes quadratiques. Premier mémoire. Sur quelques propriétés des formes quadratiques positives parfaites.
journal, January 1908
- Voronoi, Georges
- Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 1908, Issue 133
Works referencing / citing this record:
Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
journal, November 2018
- Carosso, Andrea; Hasenfratz, Anna; Neil, Ethan T.
- Physical Review Letters, Vol. 121, Issue 20
Lattice gauge theory for physics beyond the Standard Model
journal, November 2019
- Brower, Richard C.; Hasenfratz, Anna; Neil, Ethan T.
- The European Physical Journal A, Vol. 55, Issue 11