Phase transitions in a gas of anyons
Abstract
We continue our numerical Monte Carlo simulation of a gas of closed loops on a 3 dimensional lattice, however, now in the presence of a topological term added to the action which corresponds to the total linking number between the loops. We compute the linking number using a novel approach employing certain notions from knot theory. Adding the topological term converts the particles into anyons. Interpreting the model as an effective theory that describes the 2+1-dimensional Abelian Higgs model in the asymptotic strong-coupling regime, the topological linking number simply corresponds to the addition to the action of the Chern-Simons term. The system continues to exhibit a phase transition as a function of the vortex mass as it becomes small. We find the following new results. The Chern-Simons term has no effect on the Wilson loop. On the other hand, it does effect the 't Hooft loop of a given configuration, adding the linking number of the 't Hooft loop with all of the dynamical vortex loops. We find the unexpected result that both the Wilson loop and the 't Hooft loop exhibit a perimeter law even though there are no massless particles in the theory, in both phases of themore »
- Authors:
-
- Groupe de physique des particules, Departement de physique, Universite de Montreal, C.P. 6128, Succ. Centre-ville, Montreal, Quebec, H3C 3J7 (Canada)
- Reseau quebecois de calcul de haute performance, DGTIC, Universite de Montreal, C.P. 6128, Succ. Centre-ville, Montreal, Quebec, H3C 3J7 (Canada)
- Publication Date:
- OSTI Identifier:
- 21432311
- Resource Type:
- Journal Article
- Journal Name:
- Physical Review. D, Particles Fields
- Additional Journal Information:
- Journal Volume: 82; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.82.074506; (c) 2010 American Institute of Physics; Journal ID: ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANYONS; ASYMPTOTIC SOLUTIONS; COMPUTERIZED SIMULATION; CONFIGURATION; HIGGS MODEL; INSTABILITY; MASS; MASSLESS PARTICLES; MONTE CARLO METHOD; PHASE TRANSFORMATIONS; QUANTUM FIELD THEORY; STRONG-COUPLING MODEL; THREE-DIMENSIONAL CALCULATIONS; TOPOLOGY; VORTICES; WILSON LOOP; CALCULATION METHODS; ELEMENTARY PARTICLES; FIELD THEORIES; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; MATHEMATICS; PARTICLE MODELS; QUASI PARTICLES; SIMULATION
Citation Formats
MacKenzie, R, Nebia-Rahal, F, Paranjape, M B, and Richer, J. Phase transitions in a gas of anyons. United States: N. p., 2010.
Web. doi:10.1103/PHYSREVD.82.074506.
MacKenzie, R, Nebia-Rahal, F, Paranjape, M B, & Richer, J. Phase transitions in a gas of anyons. United States. https://doi.org/10.1103/PHYSREVD.82.074506
MacKenzie, R, Nebia-Rahal, F, Paranjape, M B, and Richer, J. 2010.
"Phase transitions in a gas of anyons". United States. https://doi.org/10.1103/PHYSREVD.82.074506.
@article{osti_21432311,
title = {Phase transitions in a gas of anyons},
author = {MacKenzie, R and Nebia-Rahal, F and Paranjape, M B and Richer, J},
abstractNote = {We continue our numerical Monte Carlo simulation of a gas of closed loops on a 3 dimensional lattice, however, now in the presence of a topological term added to the action which corresponds to the total linking number between the loops. We compute the linking number using a novel approach employing certain notions from knot theory. Adding the topological term converts the particles into anyons. Interpreting the model as an effective theory that describes the 2+1-dimensional Abelian Higgs model in the asymptotic strong-coupling regime, the topological linking number simply corresponds to the addition to the action of the Chern-Simons term. The system continues to exhibit a phase transition as a function of the vortex mass as it becomes small. We find the following new results. The Chern-Simons term has no effect on the Wilson loop. On the other hand, it does effect the 't Hooft loop of a given configuration, adding the linking number of the 't Hooft loop with all of the dynamical vortex loops. We find the unexpected result that both the Wilson loop and the 't Hooft loop exhibit a perimeter law even though there are no massless particles in the theory, in both phases of the theory. It should be noted that our method suffers from numerical instabilities if the coefficient of the Chern-Simons term is too large; thus, we have restricted our results to small values of this parameter. Furthermore, interpreting the lattice loop gas as an effective theory describing the Abelian Higgs model is only known to be true in the infinite coupling limit; for strong but finite coupling this correspondence is only a conjecture, the validity of which is beyond the scope of this article.},
doi = {10.1103/PHYSREVD.82.074506},
url = {https://www.osti.gov/biblio/21432311},
journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 7,
volume = 82,
place = {United States},
year = {Fri Oct 01 00:00:00 EDT 2010},
month = {Fri Oct 01 00:00:00 EDT 2010}
}