Marriage of exact enumeration and \(1/d\) expansion methods: lattice model of dilute polymers
We consider the properties of a self-avoiding polymer chain with nearest-neighbor contact energy \(\epsilon{}\) on a \(d\)-dimensional hypercubic lattice. General theoretical arguments enable us to prescribe the exact analytic form of the n-segment chain partition function \(C_n\), and unknown coefficients for chains of up to 11 segments are determined using exact enumeration data in \(d = 2-6\). This exact form provides the main ingredient to produce a large-n expansion in \(d^{-1}\) of the chain free energy through fifth order with the full dependence on the contact energy retained. The \(\epsilon{}\)-dependent chain connectivity constant and free energy amplitude are evaluated within the \(d^{-1}\) expansion to \(O(d^{-5})\). Our general formulation includes for the first time self-avoiding walks, neighbor-avoiding walks, theta, and collapsed chains as particular limiting cases.
scientific article; zbMATH DE number 111944