Marek Biskup, Christian Borgs, Jennifer T. Chayes, Logan J. Kleinwaks and Roman Kotecky
Partition function zeros at first-order phase 
transitions: A general analysis
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ABSTRACT.  We present a general, rigorous theory of partition function zeros for 
lattice spin models depending on one complex parameter. 
First, we formulate a set of natural assumptions which are verified 
for a large class of spin models in a 
companion paper. Under these assumptions, we derive 
equations whose solutions give the location of the zeros of the 
partition function with periodic boundary conditions, up to an 
error which 
we prove is (generically) exponentially small in the linear 
size of the system. For asymptotically large systems, the zeros 
concentrate on phase boundaries which are simple closed curves 
ending in multiple points. For models with 
an Ising-like plus-minus symmetry, we also establish a local 
version of the Lee-Yang Circle 
Theorem. 
This result allows us to control situations when 
in one region of the complex plane 
the zeros lie precisely on the unit circle, while in 
the complement of this region 
the zeros concentrate on less symmetric curves.