Relation between directed polymers in random media and random bond dimer models

Details Relation between directed polymers in random media and random bond dimer models Relation between directed polymers in random media and random bond dimer models

2006-06-30

arxiv.org/abs/cond-mat/0606796v1

Physics

Condensed Matter

Statistical Mechanics

6 pages, 3 figures

Scientific paper

We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. 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 hexagonal lattice. For the latter, we demonstrate the equivalence of the canonical ensemble for the dimer model and the grand-canonical description for polymers by performing explicitly the continuum limit. Using this equivalence for the random bond dimer model on a square lattice, we resolve a previously observed discrepancy between numerical results for the random dimer model and a replica approach for polymers in random media. Further potential applications of the equivalence are briefly discussed.

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