Conformational Entropy of Compact Polymers

Abstract

Exact results for the scaling properties of compact polymers on the square lattice are obtained from an effective field theory. The entropic exponent $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}117/112$ is calculated, and a line of fixed points associated with interacting chains is identified; along this line $\ensuremath{\gamma}$ varies continuously. Theoretical results are checked against detailed numerical transfer matrix calculations, which also yield a precise estimate for the connective constant $\ensuremath{\kappa}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.47280(1)$.