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

Abstract

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.

15 pages, no figures; v2: metadata corrected

References in corpus (11)

• The shape of a typical boxed plane partition
• Local statistics for random domino tilings of the Aztec diamond
• Thermodynamic limit of the Six-Vertex Model with Domain Wall Boundary Conditions
• Random Domino Tilings and the Arctic Circle Theorem
• Six-Vertex Model with Domain Wall Boundary Conditions and One-Matrix Model
• The arctic curve of the domain-wall six-vertex model
• Directed-loop Monte Carlo simulations of vertex models
• The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime
• The limit shape of large alternating sign matrices
• Lectures on the integrability of the 6-vertex model
• The Influence of Boundary Conditions in the Six-Vertex Model

Cited by in corpus (9)

• Arctic curves of the six-vertex model on generic domains: the Tangent Method
• Return probability after a quench from a domain wall initial state in the spin-1/2 XXZ chain
• Emptiness formation probability, Toeplitz determinants, and conformal field theory
• Inhomogeneous Gaussian Free Field inside the interacting arctic curve
• Artificial spin ice and vertex models
• Arctic curves of the octahedron equation
• Arctic Curves in path models from the Tangent Method
• Arctic curves of the 20V model on a triangle
• Arctic curves of the Reflecting Boundary Six Vertex and of the Twenty Vertex models