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Critical phenomena in semi-infinite systems

Published online by Cambridge University Press:  14 July 2016

J. M. Hammersley
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Abstract

This paper discusses the asymptotic behaviour, and in particular the critical singularities, of the generating functions for Pólya walks with a given fraction of visits to a hyperplane when the walk is or is not constrained to be on one side of that hyperplane. The three-dimensional case has applications in physics and chemistry.

Keywords

RANDOM WALKSPOLYMERSSURFACE ENERGYCRITICAL PHENOMENA
Type
Part 6 — Stochastic Processes
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 327 - 331
Copyright
Copyright © 1982 Applied Probability Trust 

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References

Bray, A. J. and Moore, M. A. (1977) Critical behaviour of semi-infinite systems. J. Phys. A 10, 1927–1962.Google Scholar
De Gennes, P. G. (1976) Scaling theory of polymer adsorption. J. de Physique 37, 1445–1452.Google Scholar
Hammersley, J. M., Torrie, G. M. and Whittington, S. G. (1982) Self-avoiding walks interacting with a surface. To appear.Google Scholar
Rubin, R. J. (1965) Random-walk model of chain-polymer adsorption at a surface. J. Chem. Phys. 43, 2392–2407.Google Scholar