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Entropy of covering hypercubical lattice in d dimensions by long rigid rods

Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, 2007.
Authors: D. Dhar
Editors: Luciano Pietronero and Vittorio Loreto and Stefano Zapperi
URL: http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=706
Tags: k-mers lattice long rods statistics statphys23 tilings topic-2
Abstract: We obtain upper and lower bounds on the entropy per site S(k,d), of covering all the sites of a d-dimensional lattice by straight rigid rods of length k, where k is any positive integer. Exact diagonalization of finite strips in d=2, and perturbative estimates in higher d support the conjecture that $\lim_{k \rightarrow \infty} S(k,d) k^2/\log k = 1$, for all $d$.
| URL | BibTeX  
@incollection{statphys23_0706,
title = {Entropy of covering hypercubical lattice in d dimensions by long rigid rods},
address = {Genova, Italy},
author = {D. Dhar},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
month = {9-13 July},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=706},
year = {2007},
abstract = {We obtain upper and lower bounds on the entropy per site S(k,d), of covering all the sites of a d-dimensional lattice by straight rigid rods of length k, where k is any positive integer. Exact diagonalization of finite strips in d=2, and perturbative estimates in higher d support the conjecture that $\lim_{k \rightarrow \infty} S(k,d) k^2/\log k = 1$, for all $d$.},
keywords = {k-mers lattice long rods statistics statphys23 tilings topic-2 }
}