Entropy of unimodular lattice triangulations

Beitrag in einer Fachzeitschrift

Details zur Publikation

Autorinnen und Autoren: Mecke K, Krüger B, Reinhard J
Zeitschrift: EPL - Europhysics Letters
Jahr der Veröffentlichung: 2015
Band: 109
Heftnummer: 4
ISSN: 0295-5075


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

FAU-Autorinnen und Autoren / FAU-Herausgeberinnen und Herausgeber

Krüger, Benedikt
Lehrstuhl für Theoretische Physik
Mecke, Klaus Prof. Dr.
Lehrstuhl für Theoretische Physik
Reinhard, Johannes
Lehrstuhl für Theoretische Physik


Mecke, K., Krüger, B., & Reinhard, J. (2015). Entropy of unimodular lattice triangulations. EPL - Europhysics Letters, 109(4). https://dx.doi.org/10.1209/0295-5075/109/40011

Mecke, Klaus, Benedikt Krüger, and Johannes Reinhard. "Entropy of unimodular lattice triangulations." EPL - Europhysics Letters 109.4 (2015).


Zuletzt aktualisiert 2019-24-07 um 07:28