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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:
 [1];  [1];  [1];  [2];  [2];  [3];  [3]
  1. Boston Univ., MA (United States)
  2. Yale Univ., New Haven, CT (United States)
  3. Brown Univ., Providence, RI (United States)
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:  
sc0010010; SC0015845; SC0014664; SC0010010-Task-A
Resource Type:
Published Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 98; Journal Issue: 1; Journal ID: ISSN 2470-0010
Publisher:
American Physical Society (APS)
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 Φ4 field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on S2. 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 Φ4 field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on S2. 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 Φ4 field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on S2". United States. doi:10.1103/physrevd.98.014502.
@article{osti_1459244,
title = {Lattice Φ4 field theory on Riemann manifolds: Numerical tests for the 2D Ising CFT on S2},
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: 1 work
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