Abstract
In a recent paper we derived the free energy or partition function of the N-state chiral Potts model by using the infinite lattice “inversion relation” method, together with a non-obvious extra symmetry. This gave us three recursion relations for the partition function per site T pq of the infinite lattice. Here we use these recursion relations to obtain the full Riemann surface of T pq . In terms of the t p ,t q variables, it consists of an infinite number of Riemann sheets, each sheet corresponding to a point on a (2N−1)-dimensional lattice (for N>2). The function T pq is meromorphic on this surface: we obtain the orders of all the zeros and poles. For N odd, we show that these orders are determined by the usual inversion and rotation relations (without the extra symmetry), together with a simple linearity ansatz. For N even, this method does not give the orders uniquely, but leaves only [(N+4)/4] parameters to be determined.
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Baxter, R.J. The Riemann Surface of the Chiral Potts Model Free Energy Function. Journal of Statistical Physics 112, 1–26 (2003). https://doi.org/10.1023/A:1023611702183
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DOI: https://doi.org/10.1023/A:1023611702183