Related papers: A tangent method derivation of the arctic curve fo…
We use the tangent method to investigate the arctic curve in a model of non-intersecting lattice paths with arbitrary fixed starting points aligned along some boundary and whose distribution is characterized by some arbitrary piecewise…
In the paper arXiv:1803.11463, the authors study the arctic curve arising in random tilings of some planar domains with an arbitrary distribution of defects on one edge. Using the tangent method they derive a parametric equation for…
Recently, Colomo and Sportiello introduced a powerful method, known as the \emph{Tangent Method}, for computing the arctic curve in statistical models which have a (non- or weakly-) intersecting lattice path formulation. We apply the…
The Tangent Method of Colomo and Sportiello is applied to the study of the asymptotics of domino tilings of large Aztec rectangles, with some fixed distribution of defects along a boundary. The associated Non-Intersecting Lattice Path…
We consider the four-vertex model with a special choice of fixed boundary conditions giving rise to limit shape phenomena. More generally, the considered boundary conditions relate vertex models to scalar products of off-shell Bethe states,…
Recently the first author and Jang Soo Kim introduced lecture hall tableaux in their study of multivariate little q-Jacobi polynomials. They then enumerated bounded lecture hall tableaux and showed that their enumeration is closely related…
We revisit the problem of determining the Arctic curve in the six-vertex model with domain wall boundary conditions. We describe an alternative method, by which we recover the previously conjectured analytic expression in the square domain.…
The tangent method has recently been devised by Colomo and Sportiello (arXiv:1605.01388 [math-ph]) as an efficient way to determine the shape of arctic curves. Largely conjectural, it has been tested successfully in a variety of models.…
We consider the six-vertex model in an L-shaped domain of the square lattice, with domain wall boundary conditions, in the case of free-fermion vertex weights. We describe how the recently developed `Tangent method' can be used to determine…
We use the tangent method to compute the arctic curve of the Twenty-Vertex (20V) model with particular domain wall boundary conditions for a wide set of integrable weights. To this end, we extend to the finite geometry of domain wall…
Previous numerical studies have shown that in the disordered and anti-ferroelectric phases the six-vertex ($6$V) model with partial domain wall boundary conditions (DWBC) exhibits an arctic curve whose exact shape is unknown. The model is…
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…
In this paper we consider the six-vertex model at ice point on an arbitrary three-bundle domain, which is a generalization of the domain-wall ice model on the square (or, equivalently, of a uniformly random alternating sign matrix). We show…
We apply the Tangent Method of Colomo and Sportiello to predict the arctic curves of the Six Vertex model with reflecting (U-turn) boundary and of the related Twenty Vertex model with suitable domain wall boundary conditions on a…
We apply the Tangent Method of Colomo and Sportiello to predict the arctic curves of the Twenty Vertex model with specific domain wall boundary conditions on a triangle, in the Disordered phase, leading to a phase diagram with six types of…
When applied to statistical systems showing an arctic curve phenomenon, the tangent method assumes that a modification of the most external path does not affect the arctic curve. We strengthen this statement and also make it more concrete…
We study the T-system of type $A_\infty$, also known as the octahedron recurrence/equation, viewed as a 2+1-dimensional discrete evolution equation. Generalizing the study of [P. Di Francesco and R. Soto-Garrido. Arctic curves of the…
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…
An approach to defining quadratic implicit curves is to prescribe two tangent lines and a secant line going through the points of tangency. This paper will show that this method can be generalized to a higher number of tangents, resulting…
We use the octahedron recurrence, which generalizes the quadratic recurrence found by Kuo for standard Aztec diamonds, in order to compute boundary one-refined and two-refined partition functions for two-periodic Aztec diamonds. In a first…