Conformational Entropy of Compact Polymers

TL;DR

This paper derives exact scaling properties and entropic exponents for compact polymers on a square lattice using an effective field theory, supported by numerical transfer matrix calculations.

Contribution

It provides the first exact calculation of the entropic exponent b3 for compact polymers and identifies a line of fixed points with varying b3.

Findings

Entropic exponent b3=117/112 calculated

Connective constant =1.47280(1) estimated

Line of fixed points with varying b3 identified

Abstract

Exact results for the scaling properties of compact polymers on the square lattice are obtained from an effective field theory. The entropic exponent \gamma=117/112 is calculated, and a line of fixed points associated with interacting chains is identified; along this line \gamma varies continuously. Theoretical results are checked against detailed numerical transfer matrix calculations, which also yield a precise estimate for the connective constant \kappa=1.47280(1).