A Numerical Test of KPZ Scaling: Potts Models Coupled to Two-Dimensional Quantum Gravity

Details A Numerical Test of KPZ Scaling: Potts Models Coupled to Two-Dimensional Quantum Gravity A Numerical Test of KPZ Scaling: Potts Models Coupled to Two-Dimensional Quantum Gravity

1992-04-13

arxiv.org/abs/hep-lat/9204002v1

Mod. Phys. Lett. A7 (1992) 1519

Physics

High Energy Physics

High Energy Physics - Lattice

10 pages

Scientific paper

We perform Monte Carlo simulations using the Wolff cluster algorithm of the q=2 (Ising), 3, 4 and q=10 Potts models on dynamical phi-cubed graphs of spherical topology with up to 5000 nodes. We find that the measured critical exponents are in reasonable agreement with those from the exact solution of the Ising model and with those calculated from KPZ scaling for q=3,4 where no exact solution is available. Using Binder's cumulant we find that the q=10 Potts model displays a first order phase transition on a dynamical graph, as it does on a fixed lattice. We also examine the internal geometry of the graphs generated in the simulation, finding a linear relationship between ring length probabilities and the central charge of the Potts model

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