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 formulation of 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.

arXiv comment12 pages, 1 figure, 1 table

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Cited by in corpus (6)

• Domain walls and Schramm-Loewner evolution in the random-field Ising model
• Three Dimensional Ising Model, Percolation Theory and Conformal Invariance
• Geometric Exponents, SLE and Logarithmic Minimal Models
• Percolation and Schramm-Loewner evolution in the 2D random-field Ising model
• Corner contribution to cluster numbers in the Potts model
• Corrections to scaling in geometrical clusters of the 2D Ising model