Berlin 2015 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 67: Networks: From Topology to Dynamics (joint session DY/ BP/SOE)

DY 67.6: Talk

Friday, March 20, 2015, 10:45–11:00, BH-N 128

Two-dimensional unimodular Lattice Triangulations as small-world and scale-free networks — •Benedikt Krüger, Ella Schmidt, and Klaus Mecke — Institut für Theoretische Physik, Staudtstr. 7, 91058 Erlangen

Triangulations are an important tool in physics for describing curved geometries. Unimodular triangulations on 2d lattices can also be considered as connected, simple, and maximal planar graphs, which allows the appliance of methods from graph theory on triangulations. We calculate the scaling behaviour of the degree distribution, clustering coefficient and the average shortest path length for random triangulations. Introducing a simple measure for the order of a triangulation and interpreting it as the energy of the triangulation we measure canonical averages of these observables using Monte-Carlo-Simulations. We find a crossover behaviour of all considered observables at small negative temperatures and hints for small-world and scale-free behaviour in certain temperature ranges.