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\iteman{io-port 05058246}
\itemau{Schreiber, Tomasz}
\itemti{Dobrushin-Koteck\'y-Shlosman theorem for polygonal Markov fields in the plane.}
\itemso{J. Stat. Phys. 123, No. 3, 631-684 (2006).}
\itemab
The purpose of this paper is to show that, in analogy with the Ising model, the phase separation phenomenon is present for length-interacting polygonal Markov fields and it is gouverned by the Wulff constraction [{\it T. Bodineau, D. Ioffe} and {\it I. Velenik}, Rigorous probabilistic analysis of equilibrium crystal shapes. J. Math. Phys. 41, 1033-1098 (2000; Zbl 0977.82013)]. The author considers the so-called length-interacting Arak-Surgailis polygonal Markov fields with $ V $-shaped nodes -- a continuum and isometry invariant process in the plane sharing a number of properties with the two-dimensional Ising model. It is established a low-temperature phase separation theorem in the spirit of the Dobrushin-Kotecky-Shlosman theory, with the corresponding Wulff shape determined to be a disk due to the rotation invariant nature of the considered model.
\itemrv{Nasir N. Ganikhodjaev (Kuantan)}
\itemcc{}
\itemut{phase separation; DKS theorem; Wulff shape; Arak-Surgailis polygonal Markov fields.}
\itemli{doi:10.1007/s10955-006-9053-7}
\end