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We study the solutions of the Yang-Baxter equation associated to nineteen vertex models invariant by the parity-time symmetry from the perspective of algebraic geometry. We determine the form of the algebraic curves constraining the…
Every unitary involutive solution of the quantum Yang-Baxter equation ("R-matrix") defines an extremal character and a representation of the infinite symmetric group $S_\infty$. We give a complete classification of all such Yang-Baxter…
We study generating functions of ordinary and plane partitions coloured by the action of a finite subgroup of the corresponding special linear group. After reviewing known results for the case of ordinary partitions, we formulate a…
For any positive integers $a$ and $b$, we enumerate all colored partitions made by noncrossing diagonals of a convex polygon into polygons whose number of sides is congruent to $b$ modulo $a$. For the number of such partitions made by a…
The partition function of the 2d Ising model with random nearest neighbor coupling is expressed in the dual lattice made of square plaquettes. The dual model is solved in the the mean field and in different types of Bethe-Peierls…
The Near-Bipartiteness problem is that of deciding whether or not the vertices of a graph can be partitioned into sets $A$ and $B$, where $A$ is an independent set and $B$ induces a forest. The set $A$ in such a partition is said to be an…
Yang-Baxter integrable vertex models with a generic $\mathbb{Z}_2$-staggering can be expressed in terms of composite $\mathbb{R}$-matrices given in terms of the elementary $R$-matrices. Similarly, integrable open boundary conditions can be…
It is shown that a Yang-Baxter system can be constructed from any entwining structure. It is also shown that, conversely, Yang-Baxter systems of certain type lead to entwining structures. Examples of Yang-Baxter systems associated to…
Functional equations methods are a fundamental part of the theory of Exactly Solvable Models in Statistical Mechanics and they are intimately connected with Baxter's concept of commuting transfer matrices. This concept has culminated in the…
We show that some models with non-local (and non-localizable) interactions have a property, called quasi-locality, which allows for the definition of a transfer matrix. We give the Yang-Baxter equation as a sufficient condition for the…
We compute the perturbative one-to-three Pomeron vertex in the colour glass condensate using the extended generalized leading logarithmic approximation in high energy QCD. The vertex is shown to be a conformal four-point function in…
We consider the steady-state behavior of pairs of active particles having different persistence times and diffusivities. To this purpose we employ the active Ornstein-Uhlenbeck model, where the particles are driven by colored noises with…
We consider the effect of non-reciprocity in a binary mixture of self-propelled particles with anti-aligning interactions, where a particle of type A reacts differently to a particle of type B than vice versa. Starting from a well-known…
We study the angular momentum mixing effects in the color superconductor with non-spherical pairing. We first clarify the concept of the angular momentum mixing with a toy model for non-relativistic and spinless fermions. Then we derive the…
The main aim of this paper is to determine reflections to bijective and non-degenerate solutions of the Yang-Baxter equation, by exploring their connections with their derived solutions. This is motivated by a recent description of left…
Let $R$ be a Hecke solution to the Yang-Baxter equation and $K$ be a reflection equation matrix with coefficients in an associative algebra $\A$. Let $R(x)$ be the baxterization of $R$ and suppose that $K$ satisfies a polynomial equation…
Consider a graph whose vertices are colored in one of two colors, say black or white. A white vertex is called integrated if it has at least as many black neighbors as white neighbors, and similarly for a black vertex. The coloring as a…
Connections between set-theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We show that set-theoretic $R$-matrices are expressed as twists of known solutions. We then focus on reflection and…
Every rack $Q$ provides a set-theoretic solution $c_Q$ of the Yang-Baxter equation. This article examines the deformation theory of $c_Q$ within the space of Yang-Baxter operators over a ring $\A$, a problem initiated by Freyd and Yetter in…
We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum…