Geometric and stochastic clusters of gravitating Potts models

Wolfhard Janke, Martin Weigel

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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
Issue number3-4
Publication statusPublished - 10 Aug 2006


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


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