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.
| Original language | English |
|---|---|
| Pages (from-to) | 373–377 |
| Journal | Physics Letters B |
| Volume | 639 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - 10 Aug 2006 |
Bibliographical note
NOTICE: this is the author’s version of a work that was accepted for publication in Physics Letters B. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physics Letters B, [639, 3-4, 2006] DOI: 10.1016/j.physletb.2006.06.026© 2006, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Keywords
- Potts model
- Ising model
- Quantum gravity
- Fortuin–Kasteleyn representation
- Fractal dimensions
- Annealed disorder
- Cluster algorithms