Related papers: A generalized Kac-Ward formula
The partition function of the two-dimensional Ising model with zero magnetic field on a square lattice with m x n sites wrapped on a torus is computed within the transfer matrix formalism in an explicit step-by-step approach inspired by…
A general numerical method is presented to locate the partition function zeros in the complex beta plane for large lattice sizes. We apply this method to the 2D Ising model and results are reported for square lattice sizes up tp L=64. We…
In this paper, we consider an extended Kazakov-Migdal model defined on an arbitrary graph. The partition function of the model, which is expressed as the summation of all Wilson loops on the graph, turns out to be represented by the…
The Ising model was generalized to a system of cells interacting exclusively by presence of shared spins. Within the cells there are interactions of any complexity, the simplest intracell interactions come down to the Ising model. The…
Employing the exact solution of Onsager for two-dimensional Ising models, simple expressions are proposed for computing the partition function, magnetization, specific heat and susceptibility for non-zero magnetic fields of square lattices.…
The partition function of two-dimensional nearest neighbour Ising models in a non-zero magnetic field is derived employing a matrix formulation.
We prove optimality of the Arf invariant formula for the generating function of even subgraphs, or, equivalently, the Ising partition function, of a graph.
The problem of multiway partitioning of an undirected graph is considered. A spectral method is used, where the k > 2 largest eigenvalues of the normalized adjacency matrix (equivalently, the k smallest eigenvalues of the normalized graph…
The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to…
We compute the exact partition function of the 2D Ising Model at critical temperature but with nonzero magnetic field at the boundary. The model describes a renormalization group flow between the free and fixed conformal boundary conditions…
We compute section class relative equivariant Gromov-Witten invariants of the total space of P^2-bundles of the form P(O+L1+L2)-->C where C is a genus g curve, O is the trivial bundle, and L1 (resp. L2) is an arbitrary line bundle of degree…
The large $N$ asymptotic expansion of the partition function for the normal matrix model is predicted to have special features inherited from its interpretation as a two-dimensional Coulomb gas. However for the latter, it is most natural to…
We considerably simplify Kaufman's solution of the two-dimensional Ising model by introducing two commuting representations of the complex rotation group SO(2n,C). All eigenvalues of the transfer matrix and therefore the partition function…
In 1944 Lars Onsager published the exact partition function of the ferromagnetic Ising model on the infinite square lattice in terms of a definite integral. Only in the literature of the last decade, however, has it been recast in terms of…
In this first part of a larger review undertaking the results of the first author and a part of the second author doctor dissertation are presented. Next we plan to give a survey of a nowadays situation in the area of investigation. Here we…
We perform the calculation of the partition function of the Poisson-sigma model on the world sheet with the topology of a two-dimensional disc. Considering the special case of a linear Poisson structure we recover the partition function of…
One of the most common types of functions in mathematics, physics, and engineering is a sum of products, sometimes called a partition function. After "normalization," a sum of products has a natural graphical representation, called a normal…
The simplest partition function, associated with homogeneous symmetric forms S of degree r in n variables, is integral discriminant J_{n|r}(S) = \int e^{-S(x_1 ... x_n)} dx_1 ... dx_n. Actually, S-dependence remains the same if e^{-S} in…
This paper presents an alternative proof of the connection between the partition function of the Ising model on a finite graph $G$ and the set of non-backtracking walks on $G$. The techniques used also give formulas for spin-spin…
The partition function of the two-dimensional Ising model on a square lattice with nearest-neighbour interactions and periodic boundary conditions is investigated. Kaufman [Phys. Rev. 76, 1232--1243 (1949)] gave a solution for this function…