Related papers: Two exactly soluble lattice models in three dimens…
The direct linearization structure is presented of a "mild" but significant generalization of the lattice BSQ system. Some of the equations in this system were recently discovered in [J. Hietarinta, J. Phys {\bf A}: Math. Theor. {\bf 44}…
Recent work in percolation has led to exact solutions for the site and bond critical thresholds of many new lattices. Here we show how these results can be extended to other classes of graphs, significantly increasing the number and variety…
It is well known by analysts that a concept lattice has an exponential size in the data. Thus, as soon as he works with real data, the size of the concept lattice is a fundamental problem. In this chapter, we propose to investigate factor…
We provide the exact solution of several variants of simple models of the zipping transition of two bound polymers, such as occurs in DNA/RNA, in two and three dimensions using pairs of directed lattice paths. In three dimensions the…
We review a recently developed transfer matrix formulation of the stationary scattering in two and three dimensions where the transfer matrix is a linear operator acting in an infinite-dimensional function space. We discuss its utility in…
This is a survey article on the theory of lattice points in large planar domains and bodies of dimensions 3 and higher, with an emphasis on recent developments and new methods, including a lot of results established only during the last few…
By using a decomposition of the transfer matrix of the $q$-state Potts Model on a three dimensional $ m \times n \times n $ simple cubic lattice its determinant is calculated exactly. By using the calculated determinants a formula is…
Exact and quasi-exact solvabilities of the one-dimensional Schr\"odinger equation are discussed from a unified viewpoint based on the prepotential together with Bethe ansatz equations. This is a constructive approach which gives the…
We introduce in this paper two dimensional lattice models whose continuum limit belongs to the $N=2$ series. The first kind of model is integrable and obtained through a geometrical reformulation, generalizing results known in the $k=1$…
In this paper, we study the exact solution of the $q$-deformed $D^{(1)}_3$ quantum lattice model with non-diagonal open boundary condition. We demonstrate the crossing symmetry of the transfer matrix and obtain the quantum determinant. We…
The quantum state transfer properties of a class of two-dimensional spin lattices on a triangular domain are investigated. Systems for which the 1-excitation dynamics is exactly solvable are identified. The exact solutions are expressed in…
A model describing the three-dimensional folding of the triangular lattice on the face-centered cubic lattice is generalized allowing the presence of defects corresponding to cuts in the two-dimensional network. The model can be expressed…
A simple formulation of an exactly integrable $q$-oscillator model on two dimensional lattice (in 2+1 dimensional space-time) is given. Its interpretation in the terms of 2d quantum inverse scattering method and nested Bethe Ansatz…
In the framework of the so called link approach we study exact lattice supersymmetry for the simplest supersymmetric model: N=1 supersymmetry in D=1. The model is described by a lattice with spacing a/2, thus containing twice as many sites…
We investigate the conditions under which systems of two differential eigenvalue equations are quasi exactly solvable. These systems reveal a rich set of algebraic structures. Some of them are explicitely described. An exemple of quasi…
Effective matrix methods for solving standard linear algebra problems in a commutative domains are discussed. Two of them are new. There are a methods for computing adjoined matrices and solving system of linear equations in a commutative…
We construct a variety of supersymmetric gauge theories on a spatial lattice, including N=4 supersymmetric Yang-Mills theory in 3+1 dimensions. Exact lattice supersymmetry greatly reduces or eliminates the need for fine tuning to arrive at…
Finite simplex lattice models are used in different branches of science, e.g., in condensed matter physics, when studying frustrated magnetic systems and non-Hermitian localization phenomena; or in chemistry, when describing experiments…
In our previous paper [H. K., J.Stat.Mech.(2015) P08020], we investigated an interacting-particle model with infinite-range cosine potentials, and derived the partition function which shows solid-fluid phase transition by exact calculation.…
High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product…