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Projections of Gibbs measures may be non-Gibbsian
Authors:Roberto H Schonmann
Institution:(1) Department of Mathematics, Cornell University, 14853 Ithaca, NY, USA;(2) IME-USP, Caixa Postal 20570, 01000 São Paulo SP, Brazil
Abstract:Consider the + phase of the two dimensional nearest neighbor ferromagnetic Ising model at a temperature belowT c . Let ngr+ be the restriction of this measure to a coordinate axis. We prove that there is no one dimensional translation invariant summable interaction for which ngr+ is a Gibbs measure. This is proven by showing that if such an interaction existed, ngr+ would have large deviation properties different from those it actually has. Percolation methods are used in the proof.Work supported by the U.S. Army Research Office through the Mathematical Sciences Institute at Cornell and by a NSF grant to Cornell. This work was finished while the author was visiting Rutgers University, being supported by the NSF grant 86-12369
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