Bodineau, Thierry; Schonmann, Roberto H.; Shlosman, Senya 3D crystal: how flat its flat facets are? (English) Zbl 1076.74016 Commun. Math. Phys. 255, No. 3, 747-766 (2005). Summary: We investigate the hypothesis that the (random) crystal of the \((-)\)-phase inside the \((+)\)-phase of the 3D canonical Ising model has flat facets. We argue that it might need to be weakened, due to the possibility of formation of an extra monolayer on a facet. We then prove this weaker hypothesis for the solid-on-solid model. Cited in 3 Documents MSC: 74E15 Crystalline structure 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics 05A16 Asymptotic enumeration 05A17 Combinatorial aspects of partitions of integers 74E35 Random structure in solid mechanics 82D25 Statistical mechanics of crystals Keywords:random crystal; Ising model; solid-on-solid model PDFBibTeX XMLCite \textit{T. Bodineau} et al., Commun. Math. 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