Geometric and stochastic clusters of gravitating Potts models

Wolfhard Janke, Martin Weigel

Research output: Contribution to journalArticle

Abstract

We consider the fractal dimensions of critical clusters occurring in configurations of a q-state Potts model coupled to the planar random graphs of the dynamical triangulations approach to Euclidean quantum gravity in two dimensions. For regular lattices, it is well-established that at criticality the properties of Fortuin-Kasteleyn clusters are directly related to the conventional critical exponents, whereas the corresponding properties of the geometric clusters of like spins are not. Recently it has been observed that the latter are related to the critical properties of a tricritical Potts model with the same central charge. We apply the KPZ formalism to develop a related prediction for the case of Potts models coupled to quantum gravity and employ numerical simulation methods to confirm it for the Ising case q = 2. © 2006 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)373-377
Number of pages5
JournalPhysics Letters B
Volume639
Issue number3-4
DOIs
Publication statusPublished - 10 Aug 2006

Fingerprint

gravitation
triangulation
fractals
exponents
formalism
configurations
predictions
simulation

Keywords

  • Annealed disorder
  • Cluster algorithms
  • Fortuin-Kasteleyn representation
  • Fractal dimensions
  • Ising model
  • Potts model
  • Quantum gravity

Cite this

Janke, Wolfhard ; Weigel, Martin. / Geometric and stochastic clusters of gravitating Potts models. In: Physics Letters B. 2006 ; Vol. 639, No. 3-4. pp. 373-377.
@article{ba07d33d99f8472e8df20598cbeb67d9,
title = "Geometric and stochastic clusters of gravitating Potts models",
abstract = "We consider the fractal dimensions of critical clusters occurring in configurations of a q-state Potts model coupled to the planar random graphs of the dynamical triangulations approach to Euclidean quantum gravity in two dimensions. For regular lattices, it is well-established that at criticality the properties of Fortuin-Kasteleyn clusters are directly related to the conventional critical exponents, whereas the corresponding properties of the geometric clusters of like spins are not. Recently it has been observed that the latter are related to the critical properties of a tricritical Potts model with the same central charge. We apply the KPZ formalism to develop a related prediction for the case of Potts models coupled to quantum gravity and employ numerical simulation methods to confirm it for the Ising case q = 2. {\circledC} 2006 Elsevier B.V. All rights reserved.",
keywords = "Annealed disorder, Cluster algorithms, Fortuin-Kasteleyn representation, Fractal dimensions, Ising model, Potts model, Quantum gravity",
author = "Wolfhard Janke and Martin Weigel",
year = "2006",
month = "8",
day = "10",
doi = "10.1016/j.physletb.2006.06.026",
language = "English",
volume = "639",
pages = "373--377",
journal = "Physics Letters B",
issn = "0370-2693",
publisher = "Elsevier",
number = "3-4",

}

Geometric and stochastic clusters of gravitating Potts models. / Janke, Wolfhard; Weigel, Martin.

In: Physics Letters B, Vol. 639, No. 3-4, 10.08.2006, p. 373-377.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Geometric and stochastic clusters of gravitating Potts models

AU - Janke, Wolfhard

AU - Weigel, Martin

PY - 2006/8/10

Y1 - 2006/8/10

N2 - We consider the fractal dimensions of critical clusters occurring in configurations of a q-state Potts model coupled to the planar random graphs of the dynamical triangulations approach to Euclidean quantum gravity in two dimensions. For regular lattices, it is well-established that at criticality the properties of Fortuin-Kasteleyn clusters are directly related to the conventional critical exponents, whereas the corresponding properties of the geometric clusters of like spins are not. Recently it has been observed that the latter are related to the critical properties of a tricritical Potts model with the same central charge. We apply the KPZ formalism to develop a related prediction for the case of Potts models coupled to quantum gravity and employ numerical simulation methods to confirm it for the Ising case q = 2. © 2006 Elsevier B.V. All rights reserved.

AB - We consider the fractal dimensions of critical clusters occurring in configurations of a q-state Potts model coupled to the planar random graphs of the dynamical triangulations approach to Euclidean quantum gravity in two dimensions. For regular lattices, it is well-established that at criticality the properties of Fortuin-Kasteleyn clusters are directly related to the conventional critical exponents, whereas the corresponding properties of the geometric clusters of like spins are not. Recently it has been observed that the latter are related to the critical properties of a tricritical Potts model with the same central charge. We apply the KPZ formalism to develop a related prediction for the case of Potts models coupled to quantum gravity and employ numerical simulation methods to confirm it for the Ising case q = 2. © 2006 Elsevier B.V. All rights reserved.

KW - Annealed disorder

KW - Cluster algorithms

KW - Fortuin-Kasteleyn representation

KW - Fractal dimensions

KW - Ising model

KW - Potts model

KW - Quantum gravity

UR - http://www.scopus.com/inward/record.url?scp=33746088006&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2006.06.026

DO - 10.1016/j.physletb.2006.06.026

M3 - Article

VL - 639

SP - 373

EP - 377

JO - Physics Letters B

JF - Physics Letters B

SN - 0370-2693

IS - 3-4

ER -