Related papers: The double hypergeometric series for the partition…
The aim of this article is twofold: firstly, we show how to recover the smooth Deligne-Beilinson cohomology groups from a Heegaard splitting of a closed oriented smooth 3-manifold by extending the usual \tch-de Rham construction; secondly,…
We study the three-dimensional lens partition function for $\mathcal N=2$ supersymmetric gauge dual theories on $S^3/\mathbb{Z}_r$ by using the gauge/YBE correspondence. This correspondence relates supersymmetric gauge theories to exactly…
We report an effective functional form for the spin-spin correlation function of the 2D Ising model as a function of temperature and field. Although the Ising model has been well studied, no analytical result for the spin-spin correlation…
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…
We compute the exact partition function of the isotropic 6-vertex model on a cylinder geometry with free boundary conditions, for lattices of intermediate size, using Bethe ansatz and algebraic geometry. We perform the computations in both…
This work establishes links between the Ising model and elliptic curves via Mahler measures. First, we reformulate the partition function of the Ising model on the square, triangular and honeycomb lattices in terms of the Mahler measure of…
The canonical partition function of a two-dimensional lattice gas in a field of randomly placed traps, like many other problems in physics, evaluates to the Gauss hypergeometric function ${}_2F_1(a,b;c;z)$ in the limit when one or more of…
We propose a new algorithm of the finite lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple cubic lattice from the previous…
There is no an accepted exact partition function (PF) for the three dimensional (3D) Ising model to our knowledge. Mainly based on the connection between the lattice Green function (LGF) for the simple cubic lattice and that for the…
Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their…
We suggest a generalization of the Feynman path integral to an integral over random surfaces. The proposed action is proportional to the linear size of the random surfaces and is called gonihedric. The convergence and the properties of the…
The partition function of the 2D Ising model coupled to an external magnetic field is studied. We show that the sum over the spin variables can be reduced to an integration over a finite number of variables. This integration must be…
For the generalized Ising models with all possible interactions within a face of the square lattice the formulas for finding partition function and free energy per lattice site in the thermodynamic limit were derived on a certain, in the…
The universal scaling function of the square lattice Ising model in a magnetic field is obtained numerically via Baxter's variational corner transfer matrix approach. The high precision numerical data is in perfect agreement with the…
The partition functions for two-dimensional nearest neighbour Ising model in a non-zero magnetic field have been derived for finite square lattices with the help of graph theoretical procedures, show-bit algorithm, enumeration of…
In this paper the exact solution and correlation functions for a double-chain Ising model with multi-spin interactions and symmetric Hamiltonian density are obtained. The study employs the transfer matrix method to derive fundamental…
Experimental advances in condensed matter physics and material science have enabled ready access to atomic-resolution images, with resolution of modern tools often sufficient to extract minute details of symmetry-breaking distortions such…
A new finite-size scaling approach based on the transfer matrix method is developed to calculate the critical temperature of anisotropic two-layer Ising ferromagnet, on strips of r wide sites of square lattices. The reduced internal energy…
We study dimensional crossover in Ising systems at complex temperatures by comparing three types of system: the infinite isotropic 2D Ising model; the infinite anisotropic 2D Ising model; and Ising ladders with a finite number of legs. In…
We investigate zero-field Ising models on periodic approximants of planar quasiperiodic tilings by means of partition function zeros and high-temperature expansions. These are obtained by employing a determinant expression for the partition…