Abstract
We study a system of rods onℤ2, with hard-core exclusion. Each rod has a length between 2 and N. We show that, when N is sufficiently large, and for suitable fugacity, there are several distinct Gibbs states, with orientational long-range order. This is in sharp contrast with the case N = 2 (the monomer-dimer model), for which Heilmann and Lieb proved absence of phase transition at any fugacity. This is the first example of a pure hard-core system with phases displaying orientational order, but not translational order; this is a fundamental characteristic feature of liquid crystals.
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Ioffe, D., Velenik, Y. & Zahradník, M. Entropy-Driven Phase Transition in a Polydisperse Hard-Rods Lattice System. J Stat Phys 122, 761–786 (2006). https://doi.org/10.1007/s10955-005-8085-8
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DOI: https://doi.org/10.1007/s10955-005-8085-8