Relation between directed polymers and dimer models, and its applications in spin systems
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.