On the universality of compact polymers

Abstract

Fully packed loop models on the square and the honeycomb lattice constitute new classes of critical behaviour, distinct from those of the low-temperature O(n) model. A simple symmetry argument suggests that such compact phases are only possible when the underlying lattice is bipartite. Motivated by the hope of identifying further compact universality classes we therefore study the fully packed loop model on the square-octagon lattice. Surprisingly, this model is only critical for loop weights n < 1.88, and its scaling limit coincides with the dense phase of the O(n) model. For n=2 it is exactly equivalent to the selfdual 9-state Potts model. These analytical predictions are confirmed by numerical transfer matrix results. Our conclusions extend to a large class of bipartite decorated lattices.

13 pages including 4 figures

References in corpus (4)

• Field theory of compact polymers on the square lattice
• Coupled Potts models: Self-duality and fixed point structure
• Conformational Entropy of Compact Polymers
• Compact polymers on decorated square lattices

Cited by in corpus (11)

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• Partial long-range order in antiferromagnetic Potts models
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• Active spanning trees and Schramm-Loewner evolution
• Finite average lengths in critical loop models
• The 3-edge-colouring problem on the 4-8 and 3-12 lattices
• Tiles and colors
• Hamiltonian Cycles on Ammann-Beenker Tilings
• Loop Model with Generalized Fugacity in Three Dimensions
• Two-dimensional O(n) model in a staggered field