Algebraic arctic curves in the domain-wall six-vertex model

Details Algebraic arctic curves in the domain-wall six-vertex model Algebraic arctic curves in the domain-wall six-vertex model

2010-12-12

arxiv.org/abs/1012.2555v2

J. Phys. A: Math. Theor. 44 (2011) 195201

Physics

Mathematical Physics

15 pages, no figures; v2: metadata corrected

Scientific paper

10.1088/1751-8113/44/19/195201

The arctic curve, i.e. the spatial curve separating ordered (or `frozen') and disordered (or `temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root-of-unity vertex weights. In these cases the curve is described by algebraic equations which can be worked out explicitly from the parametric solution for this curve. Some interesting examples are discussed in detail. The upper bound on the maximal degree of the equation in a generic root-of-unity case is obtained.

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