Matrix models of discretely bending, stiff polymers

Polymer models which make use of the Ising model and transfer matrix techniques remind us, for example, of the work of Flory [Statistical mechanics of chain molecules, 1969] and Zimm and Bragg [J Chem Phys, 31 (1959) 526]. We investigate the properties of some such polymer models where the chain conformation can be described solely by an Ising-like parameterization and a set of independent, predetermined bond direction vectors or by a Potts-like model for directions of bond vectors on a lattice, with the specific aim of understanding more closely the connection of constraints and forces on the chain ends for polymers which, in general, are of arc length corresponding to their persistence lengths. Instances of these models are directed helical walks, random sequential walks, bimodally distributed in direction walks or relatively short, stiff chains fixed into a network. The behavior of this model under deformation in statistical mechanics and its dynamical properties under Glauber dynamics are discussed.