Hard rigid rods on a Bethe-like lattice.
Identifieur interne : 001E50 ( PubMed/Corpus ); précédent : 001E49; suivant : 001E51Hard rigid rods on a Bethe-like lattice.
Auteurs : Deepak Dhar ; R. Rajesh ; Jürgen F. StilckSource :
- Physical review. E, Statistical, nonlinear, and soft matter physics [ 1550-2376 ] ; 2011.
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.
DOI: 10.1103/PhysRevE.84.011140
PubMed: 21867146
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pubmed:21867146Le document en format XML
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<front><div type="abstract" xml:lang="en">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.</div>
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<Abstract><AbstractText>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.</AbstractText>
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