Combinatorial Considerations on Two Models from Statistical Mechanics
2007 (English)Licentiate thesis, comprehensive summary (Other academic)
Interactions between combinatorics and statistical mechanics have provided many fruitful insights in both fields. A compelling example is Kuperberg’s solution to the alternating sign matrix conjecture, and its following generalisations. In this thesis we investigate two models from statistical mechanics which have received attention in recent years.
The first is the fully packed loop model. A conjecture from 2001 by Razumov and Stroganov opened the field for a large ongoing investigation of the O(1) loop model and its connections to a refinement of the fully packed loop model. We apply a combinatorial bijection originally found by de Gier to an older conjecture made by Propp.
The second model is the hard particle model. Recent discoveries by Fendley et al. and results by Jonsson suggests that the hard square model with cylindrical boundary conditions possess some beautiful combinatorial properties. We apply both topological and purely combinatorial methods to related independence complexes to try and gain a better understanding of this model.
Place, publisher, year, edition, pages
Matematiska institutionen , 2007. , 7 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1335
fully packed loop model, rhombus tilings, hard particle model, independence complex, discrete morse theory
IdentifiersURN: urn:nbn:se:liu:diva-10141Local ID: LIU-TEK-LIC-2007:44ISBN: 978-91-85895-44-1OAI: oai:DiVA.org:liu-10141DiVA: diva2:16889
2007-11-16, 10:15 (English)
Jonsson, Jakob, Dr.
Linusson, SvanteJonsson, Peter
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