Field theory of compact polymers on the square lattice

Abstract

Exact results for conformational statistics of compact polymers are derived from the two-flavour fully packed loop model on the square lattice. This loop model exhibits a two-dimensional manifold of critical fixed points each one characterised by an infinite set of geometrical scaling dimensions. We calculate these dimensions exactly by mapping the loop model to an interface model whose scaling limit is described by a Liouville field theory. The formulae for the central charge and the first few scaling dimensions are compared to numerical transfer matrix results and excellent agreement is found. Compact polymers are identified with a particular point in the phase diagram of the loop model, and the non-mean field value of the conformational exponent γ= 117/112 is calculated for the first time. Interacting compact polymers are described by a line of fixed points along which γvaries continuously.

32 pages (RevTeX), 11 figures in text; added further discussion of the loop ansatz. Submitted to Nucl. Phys. B [FS]

References in corpus (4)

• Critical Behavior of Random Bond Potts Models
• Critical Behaviour of Random Bond Potts Models: A Transfer Matrix Study
• Field theoretic approach to the counting problem of Hamiltonian cycles of graphs
• Folding the Square-Diagonal Lattice

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