Journal of Statistical Physics, Vol. 34, Nos. 5/6, 1984. p. 667-729.
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 a,n 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 below T c and in a field, and to the character of commensurate-incommensurate transitions for d = 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.