Geometric exponents of dilute loop models

Provencher, Guillaume, Saint-Aubin, Yvan, Pearce, Paul A. and Rasmussen, Jorgen (2012) Geometric exponents of dilute loop models. Journal of Statistical Physics, 147 2: 315-350. doi:10.1007/s10955-012-0464-3

Author Provencher, Guillaume
Saint-Aubin, Yvan
Pearce, Paul A.
Rasmussen, Jorgen
Title Geometric exponents of dilute loop models
Journal name Journal of Statistical Physics   Check publisher's open access policy
ISSN 0022-4715
Publication date 2012-04
Year available 2012
Sub-type Article (original research)
DOI 10.1007/s10955-012-0464-3
Volume 147
Issue 2
Start page 315
End page 350
Total pages 36
Place of publication New York, NY, United States
Publisher Springer
Collection year 2013
Language eng
Abstract The fractal dimensions of the hull, the external perimeter and of the red bonds are measured through Monte Carlo simulations for dilute minimal models, and compared with predictions from conformal field theory and SLE methods. The dilute models used are those first introduced by Nienhuis. Their loop fugacity is β = -2cos(π/k̄) where the parameter k̄ is linked to their description through conformal loop ensembles. It is also linked to conformal field theories through their central charges c(k̄) = 13 - 6 (k̄ + k̄ -1) and, for the minimal models of interest here, k̄ = p/p′ where p and p′ are two coprime integers. The geometric exponents of the hull and external perimeter are studied for the pairs (p,p′)=(1,1),(2,3),(3,4),(4,5),(5,6),(5,7), and that of the red bonds for (p,p′)=(3,4). Monte Carlo upgrades are proposed for these models as well as several techniques to improve their speeds. The measured fractal dimensions are obtained by extrapolation on the lattice size H,V→∞. The extrapolating curves have large slopes; despite these, the measured dimensions coincide with theoretical predictions up to three or four digits. In some cases, the theoretical values lie slightly outside the confidence intervals; explanations of these small discrepancies are proposed.
Keyword Dilute loop models
Conformal field theory
Logarithmic minimal models
Conformal loop ensembles
Fractal dimensions
Geometric exponents
Monte Carlo simulations
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Wed, 01 May 2013, 21:21:25 EST by Jorgen Rasmussen on behalf of School of Mathematics & Physics