Mecke K, Krüger B, Reinhard J (2015)
Publication Status: Published
Publication Type: Journal article
Publication year: 2015
Publisher: EPL ASSOCIATION, EUROPEAN PHYSICAL SOCIETY
Book Volume: 109
Journal Issue: 4
DOI: 10.1209/0295-5075/109/40011
Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where their entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number of possible triangulations is unknown for large systems. We present a novel algorithm for an approximate enumeration which is based on calculations of the density of states using the Wang-Landau flat histogram sampling. For triangulations on two-dimensional integer lattices we achieve excellent agreement with known exact numbers of small triangulations as well as an improvement of analytical calculated asymptotics. The entropy density is C = 2.196(3) consistent with rigorous upper and lower bounds. The presented numerical scheme can easily be applied to other counting and optimization problems. Copyright (C) EPLA, 2015
APA:
Mecke, K., Krüger, B., & Reinhard, J. (2015). Entropy of unimodular lattice triangulations. EPL - Europhysics Letters, 109(4). https://doi.org/10.1209/0295-5075/109/40011
MLA:
Mecke, Klaus, Benedikt Krüger, and Johannes Reinhard. "Entropy of unimodular lattice triangulations." EPL - Europhysics Letters 109.4 (2015).
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