caa a22 4500 467892784 CHVBK 20180406152753.0 cr unu---uuuuu 170328e20060101xx s 000 0 eng 10.1007/s10955-005-8029-3 doi (NATIONALLICENCE)springer-10.1007/s10955-005-8029-3 Rozikov U. Institute of Mathematics, 29, F.Hodjaev str., 700125, Tashkent, Uzbekistan aut A Constructive Description of Ground States and Gibbs Measures for Ising Model with Two-Step Interactions on Cayley Tree [Elektronische Daten] [U. Rozikov] We consider the Ising model with (competing) two-step interactions and spin values ± 1, on a Cayley tree of order k ≥ 1. We constructively describe ground states and verify the Peierls condition for the model. We define notion of a contour for the model on the Cayley tree. Using a contour argument we show the existence of two different Gibbs measures. Springer Science + Business Media, Inc., 2006 Cayley tree nationallicence Configuration nationallicence Ising model nationallicence Ground state nationallicence Gibbs measure nationallicence Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/2(2006-01-01), 217-235 0022-4715 122:2<217 2006 122 10955 https://doi.org/10.1007/s10955-005-8029-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8029-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rozikov U. Institute of Mathematics, 29, F.Hodjaev str., 700125, Tashkent, Uzbekistan aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/2(2006-01-01), 217-235 0022-4715 122:2<217 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer