2003/12/31 by Marek Biskup, Christian Borgs, Jennifer T. Chayes +1
Physics and Astronomy · Mathematics · #math-ph #math.CV #math.MP #msc:82B05 #msc:82B26 #msc:26C10 #msc:82B20
paper · pdf · doi:10.1023/b:joss.0000037243.48527.e3
published as J. Statist. Phys. 116 (2004), no. 1-4, 97-155 · 46 pages, 2 figs; continuation of math-ph/0304007 and math-ph/0004003, to appear in J. Statist. Phys. (special issue dedicated to Elliott Lieb)
arxiv created 2004/05/07 · arxiv updated 2009/12/01
This paper is a continuation of our previous analysis [BBCKK] of partition functions zeros in models with first-order phase transitions and periodic boundary conditions. Here it is shown that the assumptions under which the results of [BBCKK] were established are satisfied by a large class of lattice models. These models are characterized by two basic properties: The existence of only a finite number of ground states and the availability of an appropriate contour representation. This setting includes, for instance, the Ising, Potts and Blume-Capel models at low temperatures. The combined results of [BBCKK] and the present paper provide complete control of the zeros of the partition function with periodic boundary conditions for all models in the above class.