Nematic Liquid Crystal Phase in a System of Interacting Dimers and Monomers
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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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We thank Alessandro Giuliani, Diego Alberici and Daniel Ueltschi for helpful discussions about this work. The work of E.H.L. was partially supported by U.S. National Science Foundation grant PHY 1265118. The work of I.J. was supported by The Giorgio and Elena Petronio Fellowship Fund and The Giorgio and Elena Petronio Fellowship Fund II.
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