title: Hard rigid rods on a Bethe-like lattice.
abstract: We study a system of long rigid rods of fixed length k with only excluded volume interaction. We show that, contrary to the general expectation, the self-consistent field equations of the Bethe approximation do not give the exact solution of the problem on the Bethe lattice in this case. We construct a new lattice, called the random locally treelike layered lattice, which allows a dense packing of rods, and we show that the Bethe self-consistent equations are exact for this lattice. For a four-coordinated lattice, k-mers with k ≥ 4 undergo a continuous isotropic-nematic phase transition. For even coordination number q ≥ 6, the transition exists only for k ≥ k(min)(q), and is discontinuous.
authors.affiliation: Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India.
authors.forename: Deepak
authors.initials: D
authors.lastname: Dhar
authors.forename: R
authors.initials: R
authors.lastname: Rajesh
authors.forename: Jürgen F
authors.initials: JF
authors.lastname: Stilck