Field theory of compact polymers on the square lattice

TL;DR

This paper derives exact conformational statistics for compact polymers on a square lattice using a loop model mapped to Liouville field theory, revealing a non-mean field conformational exponent and a continuum of fixed points.

Contribution

It provides the first exact calculation of the conformational exponent for interacting compact polymers and links the loop model to Liouville field theory.

Findings

Exact conformational exponent b3 = 117/112 for compact polymers.

Identification of a continuum of fixed points with varying b3.

Excellent agreement between theoretical predictions and numerical transfer matrix results.

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 \gamma = 117/112 is calculated for the first time. Interacting compact polymers are described by a line of fixed points along which \gamma varies continuously.