Lattice Models of PolymersThis is a comprehensive introduction to lattice models of polymers, an important topic both in the theory of critical phenomena and the modeling of polymers. The first two chapters introduce the basic theory of random, directed and self-avoiding walks. The book then goes on to develop and expand this theory to explore the self-avoiding walk in both two and three dimensions. Following chapters describe polymers near a surface, dense polymers, self interacting polymers and branched polymers. The book closes with discussions of some geometrical and topological properties of polymers, and of self-avoiding surfaces on a lattice. The volume combines results from rigorous analytical and numerical work to give a coherent picture of the properties of lattice models of polymers. This book will be valuable for graduate students and researchers working in statistical mechanics, theoretical physics and polymer physics. It will also be of interest to those working in applied mathematics and theoretical chemistry. |
Contents
1 From polymers to random walks | 1 |
2 Excluded volume and the self avoiding walk | 19 |
3 The SAW in d 2 | 38 |
4 The SAW in d 3 | 62 |
5 Polymers near a surface | 74 |
6 Percolation | 89 |
7 Dense polymers | 104 |
Other editions - View all
Common terms and phrases
0-point adsorption average Bethe Ansatz bond branched polymers calculate chapter cluster collapse configurations conformal invariance connective constant correlation function Coulomb gas critical behaviour critical exponents critical point denote dense phase dense polymers determine directed walk discuss Duplantier edges eigenvalue equation estimate exact enumeration figure finite fixed free energy fugacity given grand canonical graph Hamiltonian walks hexagonal lattice introduced Ising model Janse van Rensburg knot lattice animals length Lett loops low temperature magnetic Manhattan lattice monomers Monte Carlo methods Nienhuis obtained Orlandini partition function percolation phase diagram Phys pivot algorithm plaquette polygons Potts model properties protein random walk regime relation renormalisation Saleur scaling spanning trees spin square lattice Stella A.L. step surface techniques term tion topology transfer matrix universality class Vanderzande vertex vertex model vertices vesicles watermelon exponents weight Whittington S.G. y-exponent