Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Monopole scaling dimension using Monte-Carlo simulation

Journal Article · · Physical Review D
 [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Department
+ Show Author Affiliations
In this paper, we present a practical Monte Carlo determination of the scaling dimensions ΔQ of flux Q Abelian monopoles through finite-size scaling analysis of the free energy to introduce the background field of classical Dirac monopole-antimonopole pair at critical points of three-dimensional lattice theories. We validate the method in free fermion theory, and by verifying the particle-vortex duality between the monopole scaling dimension at the inverse-XY fixed point and the charge scaling dimension at the XY fixed point. Finally, at the O(2) Wilson-Fisher fixed point of the XY model, we determine the critical exponents Δ1 = 0.13(2), Δ2 = 0.29(1) and Δ3 = 0.47(2), which we find to be proportional to the finite-size critical spectrum of monopoles on square torus.
Research Organization:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Organization:
USDOE; USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
Grant/Contract Number:
SC0012704
OSTI ID:
1482368
Alternate ID(s):
OSTI ID: 1480161
Report Number(s):
BNL--209454-2018-JAAM
Journal Information:
Physical Review D, Journal Name: Physical Review D Journal Issue: 7 Vol. 98; ISSN PRVDAQ; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (34)

Magnetic Monopoles book January 2005
Erratum to: Scaling dimensions of monopole operators in the ℂ ℙ N b − 1 $$ \mathrm{\mathbb{C}}{\mathrm{\mathbb{P}}}^{N_b-1} $$ theory in 2 + 1 dimensions journal March 2016
Scaling dimensions of monopole operators in the ℂ ℙ N b − 1 $$ \mathbb{C}{\mathrm{\mathbb{P}}}^{N_b-1} $$ theory in 2 + 1 dimensions journal June 2015
Monopoles in 2 + 1-dimensional conformal field theories with global U(1) symmetry journal September 2013
On the CFT operator spectrum at large global charge journal December 2015
Mandelstam-'t Hooft duality in abelian lattice models journal July 1978
Compact gauge fields and the infrared catastrophe journal October 1975
Hybrid Monte Carlo journal September 1987
Action of hedgehog instantons in the disordered phase of the (2 + 1)-dimensional CPN−1 model journal November 1990
Vortex tension as an order parameter in three-dimensional U(1) + Higgs theory journal April 1999
A duality web in 2 + 1 dimensions and condensed matter physics journal November 2016
The conformal bootstrap journal June 2016
High-precision Monte Carlo study of the 3D XY -universality class journal August 1999
Eliminating leading corrections to scaling in the three-dimensional O ( N )-symmetric ϕ 4 model: N = 3 and 4 journal October 2001
Topological Disorder Operators in Three-Dimensional Conformal Field Theory journal November 2002
Critical behavior of the three-dimensional XY universality class journal May 2001
Numerical study of duality and universality in a frozen superconductor journal January 2003
Theoretical estimates of the critical exponents of the superfluid transition in He 4 by lattice methods journal October 2006
Monopoles in CP N − 1 model via the state-operator correspondence journal December 2008
Anisotropic perturbations in three-dimensional O( N )-symmetric vector models journal September 2011
Scaling dimensions of higher-charge monopoles at deconfined critical points journal November 2015
Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators journal June 2016
Spectrum of conformal gauge theories on a torus journal May 2017
Spectrum of the Wilson-Fisher conformal field theory on the torus journal July 2017
Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics journal March 2014
No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions journal February 2016
Néel-State to Valence-Bond-Solid Transition on the Honeycomb Lattice: Evidence for Deconfined Criticality journal August 2013
Fate of C P N − 1 Fixed Points with q Monopoles journal September 2013
Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( 2 + 1 ) Dimensions journal June 2016
Universal Signatures of Quantum Critical Points from Finite-Size Torus Spectra: A Window into the Operator Content of Higher-Dimensional Conformal Field Theories journal November 2016
Conformal Dimensions via Large Charge Expansion journal February 2018
Phase Transition in a Lattice Model of Superconductivity journal November 1981
Particle-Vortex Duality from 3D Bosonization journal September 2016
An introduction to lattice gauge theory and spin systems journal October 1979

Cited By (4)

Numerical determination of monopole scaling dimension in parity-invariant three-dimensional noncompact QED journal September 2019
Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background journal November 2019
A curious behavior of three-dimensional lattice Dirac operators coupled to monopole background text January 2019
Numerical determination of monopole scaling dimension in parity-invariant three-dimensional non-compact QED text January 2019

Similar Records

Gauge fixing and extended Abelian monopoles in SU(2) gauge theory in 2+1 dimensions
Journal Article · Tue Feb 28 23:00:00 EST 1995 · Physical Review, D (Particles Fields); (United States) · OSTI ID:6853299
A duality web in condensed matter systems
Journal Article · Thu Mar 15 00:00:00 EDT 2018 · Annals of Physics · OSTI ID:22852223

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS