Dhar, Deepak ; Rajesh, R. ; Stilck, Jürgen F. (2011) Bethe approximation for a system of hard rigid rods: the random locally tree-like layered lattice Arxiv - eprints . pp. 1-10.
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Official URL: http://arxiv.org/pdf/1102.4138v1.pdf
Abstract
We study the Bethe approximation for a system of long rigid rods of fixed length k, with only excluded volume interaction. For large enough k, this system undergoes an isotropic-nematic phase transition as a function of density of the rods. The Bethe lattice, which is conventionally used to derive the self-consistent equations in the Bethe approximation, is not suitable for studying the hard-rods system, as it does not allow a dense packing of rods. We define a new lattice, called the random locally tree-like layered lattice, which allows a dense packing of rods, and for which the approximation is exact. We find that for a 4-coordinated lattice, k-mers with k ≥ 4 undergo a continuous phase transition. For even coordination number q ≥ 6, the transition exists only for k ≥ kmin(q), and is first order.
Item Type: | Article |
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Source: | Copyright of this article belongs to Arxiv Publications. |
ID Code: | 82201 |
Deposited On: | 10 Feb 2012 04:19 |
Last Modified: | 18 May 2016 23:29 |
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