Related papers: Partition Function of the Ising Model via Factor G…
The relation between the zeros of the partition function and spinodal critical points in Ising models with long-range interactions is investigated. We find the spinodal is associated with the zeros of the partition function in…
The correlation functions are calculated for the two dimensional Ising model with free boundary conditions and the two dimensional Ising model with periodic boundary conditions.
The study of zeros of partition functions, initiated by Yang and Lee, provides an important qualitative and quantitative tool in the study of critical phenomena. This has frequently been used for periodic as well as hierarchical lattices.…
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…
A method for considering a weighted directed graph with an accuracy of up to a given partition of the set of vertices is proposed. The resulting digraph (the splitting graph) does not contain arcs inside each partition element, and the arcs…
Although NP-Complete problems are the most difficult decisional problems, it is possible to discover in them polynomial (or easy) observables. We study the Graph Partitioning Problem showing that it is possible to recognize in it two…
We study the pattern of zeros emerging from exact partition function evaluations of Ising spin glasses on conventional finite lattices of varying sizes. A large number of random bond configurations are probed in the framework of quenched…
Non-Gaussian likelihoods, ubiquitous throughout cosmology, are a direct consequence of nonlinearities in the physical model. Their treatment requires Monte-Carlo Markov-chain or more advanced sampling methods for the determination of…
The class of two-spin systems contains several important models, including random independent sets and the Ising model of statistical physics. We show that for both the hard-core (independent set) model and the anti-ferromagnetic Ising…
Two objects can be distinguished if they have different measurable properties. Thus, distinguishability depends on the Physics of the objects. In considering graphs, we revisit the Ising model as a framework to define physically meaningful…
The partition function of the Ising model of a graph $G=(V,E)$ is defined as $Z_{\text{Ising}}(G;b)=\sum_{\sigma:V\to \{0,1\}} b^{m(\sigma)}$, where $m(\sigma)$ denotes the number of edges $e=\{u,v\}$ such that $\sigma(u)=\sigma(v)$. We…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
The partition function for unitary two matrix models is known to be a double KP tau-function, as well as providing solutions to the two dimensional Toda hierarchy. It is shown how it may also be viewed as a Borel sum regularization of…
Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…
The general method of graph coarsening or graph reduction has been a remarkably useful and ubiquitous tool in scientific computing and it is now just starting to have a similar impact in machine learning. The goal of this paper is to take a…
A streamlined derivation of the Kac-Ward formula for the planar Ising model's partition function is presented and applied in relating the kernel of the Kac-Ward matrices' inverse with the correlation functions of the Ising model's…
We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with…
We compute the partition functions of $\mathcal{N} = 1$ gauge theories on $S^2 \times \mathbb{R}^2_\varepsilon$ using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of $S^2$ and at the origin of…
We give an FPTAS for approximating the partition function of the hard-core model for bipartite graphs when there is sufficient imbalance in the degrees or fugacities between the sides $(L,R)$ of the bipartition. This includes, among others,…
Partition- and moment functions for a general (not necessarily Gaussian) functional measure that is perturbed by a Gibbs factor are calculated using generalized Feynman graphs. From the graphical calculus, a new notion of Wick ordering…