Nematic liquid crystal phase in a system of interacting dimers and monomers
Ian Jauslin, Elliott H. Lieb
2017
Abstract
We consider a monomer-dimer system with a strong attractive dimer-dimer interaction that favors alignment. In 1979, Heilmann and Lieb conjectured that this model should exhibit a nematic liquid crystal phase, in which the dimers are mostly aligned, but do not manifest any translational order. We prove this conjecture for large dimer activity and strong interactions. The proof follows a Pirogov-Sinai scheme, in which we map the dimer model to a system of hard-core polymers whose partition function is computed using a convergent cluster expansion.
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- tarball: 17jlC-1.0.tar.gz
- git repository: 17jlC-git (the git repository contains detailed information about the changes in the paper as well as the source code for all previous versions).
Other releases
- arXiv preprint: arXiv:1709.05297.
- This paper has been published in Communications in Mathematical Physics, Volume 363, Issue 3, pp 955-1002, doi:10.1007/s00220-018-3237-2.
Talks
This work has been presented at the following conferences:
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[AMS20]: Liquid crystals and the Heilmann-Lieb model
AMS Falls Eastern Sectional Meeting: Special session on Recent Probabilistic Advances in Mathematical Physics, online, Oct 03 2020
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[HaMPS20]: Liquid crystals and the Heilmann-Lieb model
Harvard University, Cambridge, Massachusetts, USA, Mar 31 2020
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[UBC20col]: Liquid crystals and the Heilmann-Lieb model
University of British Columbia, Vancouver, British Columbia, Canada, Jan 10 2020
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[Yal18]: Liquid crystals and the Heilmann-Lieb model
Yale University, New Haven, Connecticut, USA, Oct 11 2018
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[Har18]: Liquid crystals and the Heilmann-Lieb model
Harvard University, Boston, Massachusetts, USA, Oct 03 2018
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[ICMP18]: Liquid Crystals and the Heilmann-Lieb model
ICMP 2018, Montreal, Quebec, Canada, Jul 27 2018
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[Id18]: Liquid crystals: order upon disorder
Celebrating Ideas 2017-18, Institute for Advanced Study, Princeton, New Jersey, USA, Apr 26 2018
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[LwM18]: Liquid crystals and the Heilmann-Lieb conjecture
Lunch with a Member (IAS Friends), Institute for Advanced Study, Princeton, New Jersey, USA, Apr 06 2018
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[EL18]: Dimers, spins and loops; transfer matrices, the TL algebra and emerging Fermions
Conference celebrating Elliott Lieb's work, Princeton University, New Jersey, USA, Apr 04 2018
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[VT18]: Liquid Crystals and the Heilmann-Lieb model
VirginiaTech, Virginia, USA, Mar 21 2018
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[MCQM18]: Nematic liquid crystal phase in a system of interacting dimers
Mathematical Challenges in Quantum Mechanics 2018, Rome, Italy, Feb 23 2018
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[SMM17]: Nematic liquid crystal phase in a system of interacting dimers
118th Statistical Mechanics Meeting, Rutgers University, New Jersey, USA, Dec 17 2017
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[GT17]: Nematic liquid crystal phase in a system of interacting dimers
GeorgiaTech, Atlanta, Georgia, USA, Nov 28 2017
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[IASm17]: High density phases of hard-core lattice particle systems
Member seminar, Institute for Advanced Study, Princeton, New Jersey, USA, Oct 30 2017
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[Rut17]: High density phases of hard-core lattice particle systems
Rutgers University, New Brunswick, New Jersey, USA, Oct 26 2017
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[IAS17]: Nematic liquid crystal phase in a system of interacting dimers
Institute for Advanced Study, Princeton, New Jersey, USA, Oct 25 2017
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[IASp17]: Liquid crystals and interacting dimers
Postdoctoral talks, Institute for Advanced Study, Princeton, New Jersey, USA, Sep 29 2017
video, pdf