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Walks, walls, wetting, and melting

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Abstract

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 belowT c 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.

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  1. Baker Laboratory, Cornell University, 14853, Ithaca, New York

    Michael E. Fisher

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Fisher, M.E. Walks, walls, wetting, and melting. J Stat Phys 34, 667–729 (1984). https://doi.org/10.1007/BF01009436

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