Related papers: Some comments on developments in exact solutions i…
The anticommuting analysis with Grassmann variables is applied to the two-dimensional Ising model in statistical mechanics. The discussion includes the transformation of the partition function into a Gaussian fermionic integral, the…
We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs…
We study a three-dimensional (3D) classical Ising model that is exactly solvable when some coupling constants take certain imaginary values. The solution combines and generalizes the Onsager-Kaufman solution of the 2D Ising model and the…
We show that the two dimensional Ising model is complete, in the sense that the partition function of any lattice model on any graph is equal to the partition function of the 2D Ising model with complex coupling. The latter model has all…
In the past 30 years there have been extensive discoveries in the theory of integrable statistical mechanical models including the discovery of non-linear differential equations for Ising model correlation functions, the theory of random…
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…
Three-dimensional Ising model in zero external field is exactly solved by operator algebras, similar to the Onsager's approach in two dimensions. The partition function of the simple cubic crystal imposed by the periodic boundary condition…
A new and efficient algorithm is presented for the calculation of the partition function in the $S=\pm 1$ Ising model. As an example, we use the algorithm to obtain the thermal dependence of the magnetic spin susceptibility of an Ising…
We have provided a concise introduction to the Ising model as one of the most important models in statistical mechanics and in studying the phenomenon of phase transition. The required theoretical background and derivation of the…
We present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the "winding" technology devised by…
We study mappings between distinct classical spin systems that leave the partition function invariant. As recently shown in [Phys. Rev. Lett. 100, 110501 (2008)], the partition function of the 2D square lattice Ising model in the presence…
In this case study, we illustrate the great potential of experimental mathematics and symbolic computation, by rederiving, ab initio, Onsager's celebrated solution of the twodimensional Ising model in zero magnetic field. Onsager's…
The Ising model is an equilibrium stochastic process used as a model in several branches of science including magnetic materials, geophysics, neuroscience, sociology and finance. Real systems of interest have finite size and a fixed…
The zero-field partition function of two-dimensional nearest neighbor Ising models of square lattices is derived in terms of the generalized hypergeometric series by evaluating the integral in the exact solution of Onsager. An approximate…
This is the 13th article in the collection of reviews "Exact results in N=2 supersymmetric gauge theories", ed. J. Teschner. It discusses the relation between the instanton partition functions and the partition function of the topological…
The density of states for the three-dimensional Ising model is calculated with high-precision from multicanonical simulations. This allows us to estimate the leading partition function zeros for lattice sizes up to L=32. Combining previous…
We are describing relations between Schr\"odinger's variational problem and Onsager's approach to nonequilibrium statistical mechanics. Although the second work on reciprocal relations and detailed balance has been published in the same…
We derive an exact path integral formulation for the partition function for the Ising model using a mapping between spins and poles of a Laurent expansion for a field on the complex plane. The advantage in using this formulation for the…
The key problem of statistical physics standing over one hundred years is how to exactly calculate the partition function (or free energy) of many-body interaction systems, which severely hinders application of the theory for realistic…
We study approximations of the partition function of dense graphical models. Partition functions of graphical models play a fundamental role is statistical physics, in statistics and in machine learning. Two of the main methods for…