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Partition function zeros at first-order phase transitions: a general analysis. (English) Zbl 1088.82010
The paper is dedicated to the study of the complex phase diagram of a number of lattice spin models with one complex interaction parameter $$z$$. The basic idea is to represent the partition function $$Z^{ per}_L$$ in a box of side $$L$$ with periodic boundary conditions in the form $Z^{ per}_L (z) \simeq \sum_{m=1}^r q_m \exp(- f_m (z) L^d),$ where $$m$$ numbers phases, $$f_m$$ are not necessarily analytic functions – metastable free energies of the phases, $$q_m$$ are positive integers describing the degeneracy of the phases. A number of assumptions under which the above representation holds are formulated. Under these assumptions equations whose solutions give the location of zeros of $$Z^{ per}_L$$ are derived. It is shown that the error term is of order $$e^{-L}$$. In the limit $$L \rightarrow + \infty$$, the zeros are shown to concentrate on phase boundaries which are simple curves ending in the so called multiple points, at which more than two phases have the same value of $$f_m$$.

##### MSC:
 82B26 Phase transitions (general) in equilibrium statistical mechanics 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
##### Keywords:
Lee-Yang theorem; phase diagram; partition function zeros
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##### References:
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