caa a22 4500 46789258X CHVBK 20180406152753.0 cr unu---uuuuu 170328e20060201xx s 000 0 eng 10.1007/s10955-005-8078-7 doi (NATIONALLICENCE)springer-10.1007/s10955-005-8078-7 Random Cluster Models on the Triangular Lattice [Elektronische Daten] [L. Chayes, H. Lei] We study percolation and the random cluster model on the triangular lattice with 3-body interactions. Starting with percolation, we generalize the star-triangle transformation: We introduce a new parameter (the 3-body term) and identify configurations on the triangles solely by their connectivity. In this new setup, necessary and sufficient conditions are found for positive correlations and this is used to establish regions of percolation and non-percolation. Next we apply this set of ideas to the q > 1 random cluster model: We derive duality relations for the suitable random cluster measures, prove necessary and sufficient conditions for them to have positive correlations, and finally prove some rigorous theorems concerning phase transitions. Springer Science + Business Media, Inc., 2006 percolation nationallicence random cluster models nationallicence Potts models nationallicence star-triangle relations nationallicence FKG inequalities nationallicence Chayes L. Department of Mathematics, UCLA, Los Angeles, California, USA aut Lei H. Department of Mathematics, UCLA, Los Angeles, California, USA aut Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/4(2006-02-01), 647-670 0022-4715 122:4<647 2006 122 10955 https://doi.org/10.1007/s10955-005-8078-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8078-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chayes L. Department of Mathematics, UCLA, Los Angeles, California, USA aut NATIONALLICENCE 700 1- Lei H. Department of Mathematics, UCLA, Los Angeles, California, USA aut NATIONALLICENCE 773 0- Journal of Statistical Physics Kluwer Academic Publishers-Plenum Publishers 122/4(2006-02-01), 647-670 0022-4715 122:4<647 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer