Algebraic geometry of the three-state chiral Potts model
Brian Davies, 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 the complex numbers, 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 of 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.
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