Algebraic geometry of the three-state chiral Potts model
Brian Davies and Amnon Neeman

Abstract. 
For more than a decade now, the chiral Potts model in 
statistical mechanics has attracted much attention. A number 
of mathematical physicists have written quite extensively
about it. The solutions give rise to a curve over $\mathbb C$,
and much effort has gone into studying the curve and its
Jacobian.

In this article, we give yet another approach to this 
celebrated problem. We restrict attention to the three-state
case, which is simplest. For the first time in its history, 
we study the model with the tools from modern algebraic
geometry. Aside from simplifying and explaining the previous
results on the periods and Theta function of this curve,
we obtain a far more complete description of the Jacobian.