Marriage of exact enumeration and \(1/d\) expansion methods: lattice model of dilute polymers
type: Item
instance of: scholarly article
title: Marriage of exact enumeration and \(1/d\) expansion methods: lattice model of dilute polymers
zbMATH Open document ID: 0925.82230
DOI: 10.1007/BF01049010
author: A. M. Nemirovsky
author: Karl F. Freed
author: Takao Ishinabe
author: Jack F. Douglas
published in: Journal of Statistical Physics
publication date: 1994-09-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 82D60
Mathematics Subject Classification ID: 82B44
zbMATH DE Number: 111944
zbMATH Keywords: self-avoiding walk
zbMATH Keywords: self-interacting walk
zbMATH Keywords: neighbor-avoiding walk
zbMATH Keywords: connectivity constant
MaRDI profile type: Publication
cites work: Thermodynamics of a dense self-avoiding walk with contact interactions
full work available at URL: https://doi.org/10.1007/bf01049010
OpenAlex ID: W1999133825
description: scientific article; zbMATH DE number 111944