The Inverse Problem, Plaquette Percolation and a Generalized Potts Model.
Abstract
Three distinct problems are addressed: (1) the inverse problem in classical statistical mechanics, (2) the nature of the phase transition in a system of random plaquettes, and (3) the construction of an sstate Potts model which yields plaquette percolation in the s (>) 1 limit. The principals results are: (1) It is shown that the classical inverse problem possesses a unique solution in essentially all systems without hard core interactions, in both the canonical and grand canonical ensembles. The inverse map is shown to be continuous and, in certain cases, to be Frechet differentiable. (2) It is shown that the random plaquette system has a transition from area law to length law in all d (GREATERTHEQ) 3. Modulo a highly plausible conjecture, the absence of an intermediate phase is established in d = 3. (3) The work of Fortuin and Kasteleyn is extended to systems of random plaquettes and cells of higher dimension.
 Publication:

Ph.D. Thesis
 Pub Date:
 1983
 Bibcode:
 1983PhDT.......102C
 Keywords:

 Physics: General