Regensburg 2010 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 6: Poster Session I
DY 6.10: Poster
Monday, March 22, 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 es0mn. 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.