Related papers: Integration Approach to Ising Models
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…
We present an efficient algorithm for calculating the properties of Ising models in two dimensions, directly in the spin basis, without the need for mapping to fermion or dimer models. The algorithm gives numerically exact results for the…
The aim of the paper is to present the integrable systems on partial isometries which are related to the restricted Grassmannian in finite dimensional context. Some explicit solutions are obtained.
Let $f$ be a $r\times m$-matrix of holomorphic functions that is generically surjective. We provide explicit integral representation of holomorphic $\psi$ such that $\phi=f\psi$, provided that $\phi$ is holomorphic and annihilates a certain…
In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using…
There is no an accepted exact partition function (PF) for the two-dimensional (2D) Ising model with a non-zero external magnetic field to our knowledge. Here we infer an empirical PF for such an Ising model. We compare the PFs for two…
The previously developed n-vicinity method allows us to calculate accurately critical values of inverse temperatures for Ising models with short-range interaction. We generalize the method to the case of long-range interactions in spin…
In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under $Sp(4)$ symmetry. We establish a set of functional relations which include a transfer matrix…
Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…
We introduce and study the domain wall boundary partition function of the integrable six-vertex model with triangular boundary. We first formulate the domain wall boundary partition function with triangular boundary by using the $U_q(sl_2)$…
In this paper, we demonstrate the efficiency of simulations via direct computation of the partition function under various macroscopic conditions, such as different temperatures or volumes. The method can compute partition functions by…
We present a simple yet general and efficient approach to representation of computational meshes. Meshes are represented as sets of mesh entities of different topological dimensions and their incidence relations. We discuss a…
We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-consistency equation for nearest-neighbors' correlations. It is derived by means of an exact solution to the recurrence equations for partial…
We extend the planar Pfaffian formalism for the evaluation of the Ising partition function to lattices of high topological genus g. The 3D Ising model on a cubic lattice, where g is proportional to the number of sites, is discussed in…
The one-dimensional Ising model with nearest neighbour interactions and the zero-temperature dynamics recently considered by Lefevre and Dean -J. Phys. A: Math. Gen. {\bf 34}, L213 (2001)- is investigated. By introducing a particle-hole…
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an…
Partitions of unity in ${\mathbf R}^d$ formed by (matrix) scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
Ising model is a widely studied class of models in quantum computation. In this paper we investigate the computational characteristics of the random field Ising model (RFIM) with long-range interactions that decays as an inverse polynomial…