3 years ago

The functional method for the domain-wall partition function.

Jules Lamers

We review the (algebraic-)functional method devised by Galleas and further developed by Galleas and the author. We first explain the method for the simplest example: the computation of the partition function for the six-vertex model with domain-wall boundary conditions. At the heart of the method lies a linear functional equation for the partition function. After deriving this equation we outline its analysis. The result is a closed expression in the form of a symmetrized sum---or, equivalently, repeated contour integral---which can be rewritten to recover Izergin's determinant. We comment on the connection with the method of Korepin and Izergin, the range of applicability of the functional method, and indicate how it may be adapted to the technically more involved example of the elliptic solid-on-solid model with domain walls and a reflecting end.

Publisher URL: http://arxiv.org/abs/1801.09635

DOI: arXiv:1801.09635v1

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