  In this first part of a larger review undertaking the results of the first
author and a part of the second author doctor dissertation are presented. Next
we plan to give a survey of a nowadays situation in the area of investigation.
Here we report on what follows.
  Calculation of the partition function for any vector potts model is at first
reduced to the calculation of traces of products of the generalized clifford
algebra generators. The formula for such traces is derived. This enables one,
in principle, to use an explicit calculation algorithm for partition functions
also in other models for which the transfer matrix is an element from
generalized clifford algebra. The method - simple for $Z_2$ case - becomes
complicated for $Z_n$, $n>2$, however everything is controlled, in principle,
due to knowledge of the corresponding algebra properties and those of
generalized cosh function. The discussion of the content of the in statu
nascendi second part is to be found at the end of this presentation. This
constitutes the last section.
