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DY: Fachverband Dynamik und Statistische Physik

DY 6: Poster Session I

DY 6.10: Poster

Montag, 22. März 2010, 16:00–18:00, Poster B2

Entropy of lattice triangulations — •Johannes Reinhard and Klaus Mecke — Institut für theoretische Physik Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany

Unimodular triangulations of a rectangular planar grid of size m× n are an important tool in computational geometry and statistical physics. They have an extensive entropy in the macroscopic limit, i.e. the number of possible triangulations scales as e^s₀mn. We define an energy functional with a known ground-state degeneracy and calculate the number of triangulations using a multicanonical sampling Monte Carlo algorithm. We test the results against the exact number of triangulations, which is known for systems smaller than 6× 7. Bulk and surface terms are determined for the entropy.

Our scheme can be generalized and applied for solving approximately a multitude of combinatorial problems. As a by-product we obtain the distributions of edge-lengths and vertex-degrees in random lattice triangulations.