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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…

Mathematical Physics · Physics 2020-05-18 Bryan Debin , Philippe Di Francesco , Emmanuel Guitter

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.…

Mathematical Physics · Physics 2016-11-07 Filippo Colomo , Andrea Sportiello

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…

Mathematical Physics · Physics 2011-06-27 F. Colomo , A. G. Pronko

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,…

Mathematical Physics · Physics 2023-11-01 I. N. Burenev , F. Colomo , A. Maroncelli , A. G. Pronko

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…

Mathematical Physics · Physics 2018-04-18 Philippe Di Francesco , Matthew F. Lapa

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…

Mathematical Physics · Physics 2020-05-18 Philippe Di Francesco , Emmanuel Guitter

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…

Mathematical Physics · Physics 2023-05-10 Philippe Di Francesco

An explicit expression for the spatial curve separating the region of ferroelectric order (`frozen' zone) from the disordered one (`temperate' zone) in the six-vertex model with domain wall boundary conditions in its anti-ferroelectric…

Mathematical Physics · Physics 2015-05-14 F. Colomo , A. G. Pronko , P. Zinn-Justin

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…

Mathematical Physics · Physics 2021-09-01 Philippe Di Francesco

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…

Mathematical Physics · Physics 2020-06-23 Filippo Colomo , Andrei G. Pronko , Andrea Sportiello

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…

Mathematical Physics · Physics 2011-06-27 F. Colomo , V. Noferini , A. G. Pronko

At the free-fermion point, the six-vertex model with domain wall boundary conditions (DWBC) can be related to the Aztec diamond, a domino tiling problem. We study the mapping on the level of complete statistics for general domains and…

Statistical Mechanics · Physics 2011-11-09 Patrik L. Ferrari , Herbert Spohn

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…

Probability · Mathematics 2022-02-17 Amol Aggarwal

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…

Mathematical Physics · Physics 2018-10-22 Philippe Di Francesco , Emmanuel Guitter

We use a tangent method approach to obtain the arctic curve in a model of non-intersecting lattice paths within the first quadrant, including a q-dependent weight associated with the area delimited by the paths. Our model is characterized…

Mathematical Physics · Physics 2019-02-20 Philippe Di Francesco , Emmanuel Guitter

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…

Mathematical Physics · Physics 2020-01-30 Bryan Debin , Philippe Ruelle

The partition function of the six-vertex model on a square lattice with domain wall boundary conditions (DWBC) is rewritten as a hermitean one-matrix model or a discretized version of it (similar to sums over Young diagrams), depending on…

Mathematical Physics · Physics 2009-10-31 P. Zinn-Justin

We compute the algebraic equation for arctic curves of the Aztec diamond with a doubly (quasi-)periodic weight structure and obtain similar results for certain models of the hexagon. In particular, we determine the algebraic degree of such…

Mathematical Physics · Physics 2024-10-23 Mateusz Piorkowski

The purpose of the present work is to provide a detailed asymptotic analysis of the $k\times\ell$ doubly periodic Aztec diamond dimer model of growing size for any $k$ and $\ell$ and under mild conditions on the edge weights. We explicitly…

Probability · Mathematics 2023-08-23 Tomas Berggren , Alexei Borodin

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…

Combinatorics · Mathematics 2021-01-13 Sylvie Corteel , David Keating , Matthew Nicoletti
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