Related papers: Boundary polarization in the six-vertex model

We study the partition function for the three-colour model with domain wall boundary conditions. We express it in terms of certain special polynomials, which can be constructed recursively. Our method generalizes Kuperberg's proof of the…

We show that in boundary CFTs, there exists a one-to-one correspondence between the boundary operator expansion of the two-point correlation function and a power series expansion of the layer susceptibility. This general property allows the…

Following Barany et al., who proved that large random lattice zonotopes converge to a deterministic shape in any dimension after rescaling, we establish a central limit theorem for finite-dimensional marginals of the boundary of the…

The large scale fluctuations of the ordered state in active matter systems are usually characterised by studying the "giant number fluctuations" of particles in any finite volume, as compared to the expectations from the central limit…

In two-dimensional statistical physics, correlation functions of the O(N) and Potts models may be written as sums over configurations of non-intersecting loops. We define sums associated to a large class of combinatorial maps (also known as…

This is a continuation of the papers [4] of Bleher and Fokin and [5] of Bleher and Liechty, in which the large $n$ asymptotics is obtained for the partition function $Z_n$ of the six-vertex model with domain wall boundary conditions in the…

In this paper we consider a class of probability distributions on the six-vertex model from statistical mechanics, which originate from the higher spin vertex models of https://arxiv.org/abs/1601.05770. We define operators, inspired by the…

We continue the work of Belliard, Pimenta and Slavnov (2024) studying the modified rational six vertex model. We find another formula of the partition function for the inhomogeneous model, in terms of a determinant that mix the modified…

The solution of constrained linear partial-differential equations can be described via parametric representations of linear relations. To study these representations, we provide a novel definition of boundary triplets for linear relations…

We study the relationship between various integral formulas for nonlocal correlation functions of the six-vertex model with domain wall boundary conditions. Specifically, we show how the known representation for the emptiness formation…

We define a correlation function that quantifies the spatial correlation of single-particle displacements in liquids and amorphous materials. We show for an equilibrium liquid that this function is related to fluctuations in a bulk…

We diagonalise the transfer matrix of boundary ABF models using bosonized vertex operators. We compute the boundary S-matrix and check the scaling limit against known results for perturbed boundary conformal field theories.

The question of boundary conditions in conformal field theories is discussed, in the light of recent progress. Two kinds of boundary conditions are examined, along open boundaries of the system, or along closed curves or ``seams''. Solving…

The correlation term, introduced in [13] to describe the interaction between very far apart vortices, governs symmetry-breaking for the Ginzburg-Landau equation in R^2 or bounded domains. It is a homogeneous function of degree (-2), and…

We propose an operational degree of polarization in terms of the variance of the projected Stokes vector minimized over all the directions of the Poincar\'e sphere. We examine the properties of this degree and show that some problems…

The scaling limit of the spectrum, $S$ matrix, and of the form factors of the polarization operator in the six vertex model has been found. The result for the form factors is consistent with the form factors of the sine-Gordon model found…

We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal…

Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full…

Ordered polarity alignment of a cell population plays a vital role in biology, such as in hair follicle alignment and asymmetric cell division. Here, we propose a theoretical framework for the understanding of generic dynamical properties…

We examine fluctuations of vorticity excited by an external random force in two-dimensional fluid in the presence of a strong external shear flow. The problem is motivated by the analysis of big coherent vortices appearing as a consequence…