Related papers: Recursion relations for the partition function of …
We study a family of inhomogeneous Ising chain models along with an equivalent family of nearest neighbour particle systems. By the correspondence between the two families we prove identities of combinatorial significance relating to…
Finite size effects for the Ising Model coupled to two dimensional random surfaces are studied by exploiting the exact results from the 2-matrix models. The fixed area partition function is numerically calculated with arbitrary precision by…
In this paper we present a new solution of the star-triangle relation having positive Boltzmann weights. The solution defines an exactly solvable two-dimensional Ising-type (edge interaction) model of statistical mechanics where the local…
This paper deals with the partition function of the Ising model from statistical mechanics, which is used to study phase transitions in physical systems. A special case of interest is that of the Ising model with constant energies and…
Correlation functions of the two-dimensional Ising model on the periodic lattice can be expressed in terms of form factors - matrix elements of the spin operator in the basis of common eigenstates of the transfer matrix and translation…
We present an implementation of the method of orthogonal polynomials which is particularly suitable to study the partition functions of Penner random matrix models, to obtain their explicit forms in the exactly solvable cases, and to…
Multiple orthogonal polynomials satisfy a number of recurrence relations, in particular there is a $(r+2)$-term recurrence relation connecting the type II multiple orthogonal polynomials near the diagonal (the so-called step-line recurrence…
An integrable system is often formulated as a flat connection, satisfying a Lax equation. It is given in terms of compatible systems having a common solution called the ``wave function" $\Psi$ living in a Lie group $G$, which satisfies some…
The high-performance scalable parallel algorithm for rigorous calculation of partition function of lattice systems with finite number Ising spins was developed. The parallel calculations run by C++ code with using of Message Passing…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
We revisit the classical transfer matrix solution of the one- and two-dimensional Ising model from the perspective of Clifford and conformal geometric algebras. Building on Kaufman's spinor formulation, we show that all elements entering…
Spin networks appear in a number of areas, for instance in lattice gauge theories and in quantum gravity. They describe the contraction of intertwiners according to the underlying network. We show that a certain generating function of…
We consider a two-dimensional bi-layered loop model with a certain interlayer coupling and study its spectrum on a torus. Each layer consists of an $O(n)$ model on a honeycomb lattice with periodic boundary conditions; these layers are…
The aim of this work is to present a formulation to solve the one-dimensional Ising model using the elementary technique of mathematical induction. This formulation is physically clear and leads to the same partition function form as the…
We derive the recurrence relations for relativistic Coulomb integrals directly from the integral representations with the help of computer algebra methods. In order to manage the computational complexity of this problem, we employ holonomic…
We consider Kingman's partition structures which are regenerative with respect to a general operation of random deletion of some part. Prototypes of this class are the Ewens partition structures which Kingman characterised by regeneration…
We introduce the subsum polynomial of a partition $\lambda=(\lambda_1, \lambda_2, \ldots, \lambda_k)$ defined by $\mathrm{sp}(\lambda, x)=\prod_{i=1}^k(1+x^{\lambda_i})$. We study the sum of reciprocals of $\mathrm{sp}(\lambda, x)$ over all…
In this note we overview recent convergence results for correlations in the critical planar nearest-neighbor Ising model. We start with a short discussion of the combinatorics of the model and a definition of fermionic and spinor…
In this paper, we study three applications of recursion to problems in coding and random permutations. First, we consider locally recoverable codes with partial locality and use recursion to estimate the minimum distance of such codes. Next…
A close connection of reverse plane partitions with an integrable dynamical system called the discrete two-dimensional (2D) Toda molecule is clarified. It is shown that a multiplicative partition function for reverse plane partition of…