The statistical mechanics of interacting walks, polygons, animals and vesicles
著者
書誌事項
The statistical mechanics of interacting walks, polygons, animals and vesicles
（Oxford lecture series in mathematics and its applications, 39）
Oxford University Press, 2015
2nd ed.
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics. It is also a simple model of polymer entropy which is useful in modelling phase behaviour in polymers.
This monograph provides an authoritative examination of interacting self-avoiding walks, presenting aspects of the thermodynamic limit, phase behaviour, scaling and critical exponents for lattice polygons, lattice animals and surfaces. It also includes a comprehensive account of constructive methods in models of adsorbing, collapsing, and pulled walks, animals and networks, and for models of walks in confined geometries. Additional topics include scaling, knotting in lattice polygons,
generating function methods for directed models of walks and polygons, and an introduction to the Edwards model.
This essential second edition includes recent breakthroughs in the field, as well as maintaining the older but still relevant topics. New chapters include an expanded presentation of directed models, an exploration of methods and results for the hexagonal lattice, and a chapter devoted to the Monte Carlo methods.
目次
- 1. Lattice models of linear and ring polymers
- 2. Lattice models of branched polymers
- 3. Interacting lattice clusters
- 4. Scaling, criticality and tricriticality
- 5. Directed lattice paths
- 6. Convex lattice vesicles and directed animals
- 7. Self-avoiding walks and polygons
- 8. Self-avoiding walks in slabs and wedges
- 9. Interaction models of self-avoiding walks
- 10. Adsorbing walks in the hexagonal lattice
- 11. Interacting models of animals, trees and networks
- 12. Interacting models of vesicles and surfaces
- 13. Monte Carlo methods for the self-avoiding walk
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