The Z_n Baxter model is an exactly solvable lattice model in the special case of the Belavin parametrization. For this parametrization we calculate the partition function, x, in an antiferromagnetic region and the order parameter in a ferromagnetic region. We find that the order parameter is expressible in terms of a modular function of level n which for n = 2 is the Onsager-Yang-Baxter result. In addition we determine the symmetry group of the finite lattice partition function for the general Z_n Baxter model
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