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

Abstract

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.

6 pages, 3 figures

References in corpus (7)

• Three dimensional resonating valence bond liquids and their excitations
• Interacting classical dimers on the square lattice
• Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors
• Ordering of geometrically frustrated classical and quantum Ising magnets
• String Picture of a Frustrated Quantum Magnet and Dimer Model
• Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder
• Is there a Glass Transition in Planar Vortex Systems?

Cited by in corpus (1)

• Classical dimer model with anisotropic interactions on the square lattice