Combinatorial considerations on two models from statistical mechanics / Johan Thapper.
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Thapper, Johan, 1977- (författare)
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- Linköpings universitet. Matematiska institutionen (utgivare)
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Alternativt namn: Linköpings universitet. Tekniska högskolan. Matematiska institutionen
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Alternativt namn: Linköping University. Department of Mathematics
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Alternativt namn: MAI
- ISBN 9789185895441
- Publicerad: Linköping : Matematiska institutionen, Linköpings universitet, 2007
- Engelska vi, 79 s.
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Serie: Linköping studies in science and technology. Thesis, 0280-7971 ; 1335
- Relaterad länk:
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http://urn.kb.se/res... (Sammanfattning och ramberättelse från Linköping University Electronic Press)
Sammanfattning
Ämnesord
Stäng
- 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.
Ämnesord
- Kombinatorik (sao)
- Statistisk mekanik (sao)
- Combinatorial analysis (LCSH)
- Statistical mechanics (LCSH)
Genre
- Avhandlingar (saogf)
Indexterm och SAB-rubrik
- Fully packed loop mode
- Rhombus tilings
- Hard particle model
- Independence complex
- Discrete morse theory
- Tce Kombinatorik
- Uccec Statistisk mekanik
Klassifikation
- 511.6 (DDC)
- 530.13 (DDC)
- Tce (kssb/8)
- Uccec (kssb/8)
Inställningar
Hjälp
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