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arXiv:1510.00342 · Nuclear Physics B

Integral formula for elliptic SOS models with domain walls and a reflecting end

Jules Lamers

Published Nov 11, 2015• 8 citations
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Abstract

In this paper we extend previous work of Galleas and the author to elliptic sos models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an elliptic sos model with domain-wall boundaries and one reflecting end. Special attention is paid to the structure of the functional equation. Through this approach we find a novel multiple-integral formula for that partition function.

DOI
10.1016/j.nuclphysb.2015.11.006

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In this paper we extend previous work of Galleas and the author to elliptic sos models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an elliptic sos model with domain-wall boundaries and one reflecting end. Special attention is paid to the structure of the functional equation. Through this approach we find a novel multiple-integral formula for that partition function.
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In this work we investigate the possibility of using the reflection algebra as a source of functional equations. More precisely, we obtain functional relations determining the partition function of the six-vertex model with domain-wall boundary conditions and one reflecting end. The model's partition function is expressed as a multiple-contour integral that allows the homogeneous limit to be obtained straightforwardly. Our functional equations are also shown to give rise to a consistent set of partial differential equations satisfied by the partition function.
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