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Entropy-driven Phase Transition in a Polydisperse Hard-rods Lattice System D. Ioffe, Y. Velenik and M. Zahradník J. Stat. Phys. 122, no. 4, 761-786 (2006). We study a system of rods on $\mathbb{Z}^2$, 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. Key words: Hard-rods, monomer-dimer model, nematic order, liquid crystal. Files: PDF file, published version, bibtex