Relation between directed polymers and dimer models, and its applications in spin systems
Y. Jiang, and T. Emig. Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
The relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers is investigated. In the absence of randomness, we determine the density and line tension of the polymers in terms of the bond weights of hard-core dimers on the square and the honeycomb lattice. For the latter, we demonstrate the equivalence of the set of complete dimer coverings and the grand-canonical description of polymers by performing explicitly the continuum limit. By use of this equivalence for the random-bond dimer model on a square lattice, a previously observed discrepancy between numerical results for the random dimer model and a replica approach for polymers in random media is resolved. Further potential applications in geometrically frustrated Ising antiferromagnets are briefly discussed.
%0 Book Section
%1 statphys23_0513
%A Jiang, Y.
%A Emig, T.
%B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics
%C Genova, Italy
%D 2007
%E Pietronero, Luciano
%E Loreto, Vittorio
%E Zapperi, Stefano
%K dimer disorder frustrated geometrically models polymers quenched random-bond spin statphys23 system topic-9
%T Relation between directed polymers and dimer models, and its applications in spin systems
%U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=513
%X The relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers is investigated. In the absence of randomness, we determine the density and line tension of the polymers in terms of the bond weights of hard-core dimers on the square and the honeycomb lattice. For the latter, we demonstrate the equivalence of the set of complete dimer coverings and the grand-canonical description of polymers by performing explicitly the continuum limit. By use of this equivalence for the random-bond dimer model on a square lattice, a previously observed discrepancy between numerical results for the random dimer model and a replica approach for polymers in random media is resolved. Further potential applications in geometrically frustrated Ising antiferromagnets are briefly discussed.
@incollection{statphys23_0513,
abstract = {The relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers is investigated. In the absence of randomness, we determine the density and line tension of the polymers in terms of the bond weights of hard-core dimers on the square and the honeycomb lattice. For the latter, we demonstrate the equivalence of the set of complete dimer coverings and the grand-canonical description of polymers by performing explicitly the continuum limit. By use of this equivalence for the random-bond dimer model on a square lattice, a previously observed discrepancy between numerical results for the random dimer model and a replica approach for polymers in random media is resolved. Further potential applications in geometrically frustrated Ising antiferromagnets are briefly discussed.},
added-at = {2007-06-20T10:16:09.000+0200},
address = {Genova, Italy},
author = {Jiang, Y. and Emig, T.},
biburl = {https://www.bibsonomy.org/bibtex/29cbd17b4a241da4f633d9fc5d2496a1b/statphys23},
booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano},
interhash = {ff34f4516a22b54d3493934dc5a33ea5},
intrahash = {9cbd17b4a241da4f633d9fc5d2496a1b},
keywords = {dimer disorder frustrated geometrically models polymers quenched random-bond spin statphys23 system topic-9},
month = {9-13 July},
timestamp = {2007-06-20T10:16:22.000+0200},
title = {Relation between directed polymers and dimer models, and its applications in spin systems},
url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=513},
year = 2007
}