The arctic curve of the domain-wall six-vertex model

Understand

The problem of the form of the `arctic' curve of the six-vertex model with domain wall boundary conditions in its disordered regime is addressed.

• It is well-known that in the scaling limit the model exhibits phase-separation, with regions of order and disorder sharply separated by a smooth curve, called the arctic curve.
• To find this curve, we study a multiple integral representation for the emptiness formation probability, a correlation function devised to detect spatial transition from order to disorder.
• We conjecture that the arctic curve, for arbitrary choice of the vertex weights, can be characterized by the condition of condensation of almost all roots of the corresponding saddle-point equations at the same, known, value.