Partition function zeros of the one-dimensional Potts model: The recursive method

  • Ghulghazaryan R
  • Ananikian N
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Abstract

The Yang–Lee, Fisher and Potts zeros of the one-dimensional
Q -state Potts model are studied using the theory of dynamical systems.
An exact recurrence relation for the partition function is derived.
It is shown that zeros of the partition function may be associated
with neutral fixed points of the recurrence relation. Further, a
general equation for zeros of the partition function is found and
a classification of the Yang–Lee, Fisher and Potts zeros is
given. It is shown that the Fisher zeros in a nonzero magnetic field
are located on several lines in the complex temperature plane and
that the number of these lines depends on the value of the magnetic
field. Analytical expressions for the densities of the Yang–Lee,
Fisher and Potts zeros are derived. It is shown that densities of
all types of zeros of the partition function are singular at the
edge singularity points with the same critical exponent σ
&equal; −½.

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