Journal of Statistical Physics

, Volume 34, Issue 5–6, pp 667–729 | Cite as

Walks, walls, wetting, and melting

  • Michael E. Fisher


New results concerning the statistics of, in particular,p random walkers on a line whose paths do not cross are reported, extended, and interpreted. A general mechanism yielding phase transitions in one-dimensional or linear systems is recalled and applied to various wetting and melting phenomena in (d=2)-dimensional systems, including fluid films and p×1 commensurate adsorbed phases, in which interfaces and domain walls can be modelled by noncrossing walks. The heuristic concept of an effective force between a walk and a rigid wall, and hence between interfaces and walls and between interfaces, is expounded and applied to wetting in an external field, to the behavior of the two-point correlations of a two-dimensional Ising model belowTc and in a field, and to the character of commensurate-incommensurate transitions ford=2 (recapturing recent results by various workers). Applications of random walk ideas to three-dimensional problems are illustrated in connection with melting in a lipid membrane model.

Key words

Walks (random and vicious) walls (of domains and containers) wetting (transitions in two dimensions) melting (of adsorbed surface phases) 


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Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • Michael E. Fisher
    • 1
  1. 1.Baker LaboratoryCornell UniversityIthaca

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