05-95 D. Ioffe, Y. Velenik, M. Zahradn k

Entropy-driven Phase Transition in a Polydisperse Hard-rods Lattice System (448K, pdf) Mar 8, 05

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Abstract. We study a system of rods on the square lattice, 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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