Six-vertex model with partial domain wall boundary conditions: Ferroelectric phase

Abstract

Abstract. We obtain an asymptotic formula for the partition function of the six-vertex model with partial domain wall boundary conditions in the ferroelectric phase region. The proof is based on a formula for the partition function involving the determinant of a matrix of mixed Vandermonde/Hankel type. This determinant can be expressed in terms of a system of discrete orthogonal polynomials, which can then be evaluated asymptotically by comparison with the Meixner polynomials.

Phase separation in the six-vertex model with a variety of boundary conditions

“…We modified the original AR algorithm, to address the study of pDWBC, the six-vertex model with a RE and HTBC. In some cases [23,28,29], exact results for the partition functions were known in the thermodynamic limit but the presence of phase separation and the shape of the arctic curve have been never investigated. We show that when the model has only two parameters a and b, typical configurations display features similar to DWBC, varying ∆ in Eq.…”

The density profile of the six vertex model with domain wall boundary conditions

“…Many generalizations are possible and are currently under investigation by the authors. Among them we mention the study of the phase diagram for other type of boundary conditions like alternating boundary conditions [40,41] or partial domain wall boundary conditions [42,43]. The algorithm can also easily be adapted to lattices of different shape, such as an L-shape [44].…”

Domain Wall Six-Vertex Model with Half-Turn Symmetry

“…Outside of these special weights, the relevant orthogonal polynomials are not classical but may be analyzed asymptotically using the Riemann-Hilbert method. This approach has been employed by the current authors and their collaborators to obtain exact asymptotic formulas for the partition function of the six-vertex model with DWBC as well as partial domain wall boundary conditions (pDWBC) [3,4,5,6,1,2,7,8]. This paper continues that program, extending the asymptotic analysis of the DWBC partition function employed in previous works to a six-vertex model with DWBC which is further constrained by a rotational symmetry.…”