Dresden 2009 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 13: Statistical physics III (general)
DY 13.1: Vortrag
Dienstag, 24. März 2009, 14:45–15:00, ZEU 255
Searching phase transitions in lattice triangulations — •Johannes Reinhard and Klaus Mecke — Institut für Theoretische Physik Universität Erlangen-Nürnberg, Staudtstrasse 7, 91058 Erlangen, Germany
The number of unimodular triangulations of the planar grid with size m× n scales as ∼ es0 mn. This allows the definition of a statistical model of random planar graphs in analogy to the Ising model. Instead of spin configurations on a fixed grid we consider triangulations with random edge lengths and coordination numbers at each grid point. The Hamiltonian of a triangulation includes the sum over all edge lengths and powers of the coordination numbers. We study the geometric and topological properties of this ensemble of lattice triangulations by a Monte-Carlo simulation based on an ergodic edge-flip dynamics. A transition is observed between a disordered and an ordered state of triangulations.