caa a22 4500 467891931 CHVBK 20180406152751.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s10955-006-9053-7 doi (NATIONALLICENCE)springer-10.1007/s10955-006-9053-7 Schreiber Tomasz Faculty of Mathematics & Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland aut Dobrushin-Kotecký-Shlosman Theorem for Polygonal Markov Fields in the Plane [Elektronische Daten] [Tomasz Schreiber] We consider 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. For these polygonal fields we establish a low-temperature phase separation theorem in the spirit of the Dobrushin-Kotecký-Shlosman theory, with the corresponding Wulff shape deteremined to be a disk due to the rotation invariant nature of the considered model. As an important tool replacing the classical cluster expansion techniques and very well suited for our geometric setting we use a graphical construction built on contour birth and death process, following the ideas of Férnandez, Ferrari and Garcia. Springer Science+Business Media, Inc., 2006 phase separation nationallicence DKS theorem nationallicence Wulff shape nationallicence Arak-Surgailis polygonal Markov fields nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/3(2006-05-01), 631-684 0022-4715 123:3<631 2006 123 10955 https://doi.org/10.1007/s10955-006-9053-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9053-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Schreiber Tomasz Faculty of Mathematics & Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 123/3(2006-05-01), 631-684 0022-4715 123:3<631 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer