Faculté des sciences

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

Jiang, Ying ; Emig, Thorsten

In: Physical Review B, 2007, vol. 75, p. 134413

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 honeycomb lattice. For the latter, we demonstrate the equivalence of the set of complete dimer... Plus

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    Summary
    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 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. 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.