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Title: Monopole scaling dimension using Monte-Carlo simulation

Abstract

In this paper, we present a practical Monte Carlo determination of the scaling dimensions Δ Q 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 Δ 1 = 0.13(2), Δ 2 = 0.29(1) and Δ 3 = 0.47(2), which we find to be proportional to the finite-size critical spectrum of monopoles on square torus.

Authors:
 [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Department
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)
OSTI Identifier:
1482368
Alternate Identifier(s):
OSTI ID: 1480161
Report Number(s):
BNL-209454-2018-JAAM
Journal ID: ISSN 2470-0010; PRVDAQ
Grant/Contract Number:  
SC0012704
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 98; Journal Issue: 7; 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

Karthik, Nikhil. Monopole scaling dimension using Monte-Carlo simulation. United States: N. p., 2018. Web. doi:10.1103/PhysRevD.98.074513.
Karthik, Nikhil. Monopole scaling dimension using Monte-Carlo simulation. United States. doi:10.1103/PhysRevD.98.074513.
Karthik, Nikhil. Wed . "Monopole scaling dimension using Monte-Carlo simulation". United States. doi:10.1103/PhysRevD.98.074513.
@article{osti_1482368,
title = {Monopole scaling dimension using Monte-Carlo simulation},
author = {Karthik, Nikhil},
abstractNote = {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.},
doi = {10.1103/PhysRevD.98.074513},
journal = {Physical Review D},
issn = {2470-0010},
number = 7,
volume = 98,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on October 31, 2019
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