Related papers: Some Exact Results on the Potts Model Partition Fu…

We propose a method for generalizing the Ising model in magnetic fields and calculating the partition function (exact solution) for the Ising model of an arbitrary shape. Specifically, the partition function is calculated using matrices…

This paper surveys a comprehensive, although not exhaustive, sampling of graph polynomials with the goal of providing a brief overview of a variety of techniques defining a graph polynomial and then for decoding the combinatorial…

The remarkable properties of the real scalar quartic quantum field theory on the Moyal plane in combination with its similarity to the Kontsevich model make the model's partition function an interesting object to study. However, direct…

In this note we study the block spin mean-field Potts model, in which the spins are divided into $s$ blocks and can take $q\ge 2$ different values (colors). Each block is allowed to contain a different proportion of vertices and behaves…

Higher genus partition functions of two-dimensional conformal field theories have to be invariants under linear actions of mapping class groups. We illustrate recent results [4,6] on the construction of such invariants by concrete…

In this paper, we find computational formulae for generalized characteristic polynomials of graph bundles. We show that the number of spanning trees in a graph is the partial derivative (at (0,1)) of the generalized characteristic…

We give an especially simple proof of a theorem in graph theory that forms the key part of the solution to a problem in commutative algebra, on how to characterize the integral closure of a polynomial ring generated by quadratic monomials.

The partition function and magnetization equations are derived for the two-dimensional nearest neighbour Ising models in a magnetic field.

We study a log-gas on a network (a finite, simple graph) confined in a bounded subset of a local field (i.e. R, C, Q_{p} the field of p-adic numbers). In this gas, a log-Coulomb interaction between two charged particles occurs only when the…

The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising…

Biskup et al. [Phys. Rev. Lett. 84 (2000) 4794] have recently suggested that the loci of partition function zeroes can profitably be regarded as phase boundaries in the complex temperature or field planes. We obtain the Fisher zeroes for…

We present a new approach to a classical problem in statistical physics: estimating the partition function and other thermodynamic quantities of the ferromagnetic Ising model. Markov chain Monte Carlo methods for this problem have been…

The complexity of graph homomorphism problems has been the subject of intense study. It is a long standing open problem to give a (decidable) complexity dichotomy theorem for the partition function of directed graph homomorphisms. In this…

The partition function of a factor graph can sometimes be accurately estimated by Monte Carlo methods. In this paper, such methods are extended to factor graphs with negative and complex factors.

We present both analytic and numerical results on the position of the partition function zeros on the complex magnetic field plane of the $q=2$ (Ising) and $q=3$ states Potts model defined on $\phi^3 $ Feynman diagrams (thin random graphs).…

Given an infinite graph $\GI$ quasi-transitive and amenable with maximum degree $\D$, we show that reduced ground state degeneracy per site $W_r(\GI,q)$ of the q-state antiferromagnetic Potts model at zero temperature on $\GI$ is analytic…

We prove optimality of the Arf invariant formula for the generating function of even subgraphs, or, equivalently, the Ising partition function, of a graph.

We construct the exact partition function of the Potts model on a complete graph subject to external fields with linear and nematic type couplings. The partition function is obtained as a solution to a linear diffusion equation and the free…

Let $Z_n(z,t)$ denote the partition function of the $q$-state Potts Model on the rooted binary Cayley tree of depth~$n$. Here, $z = {\rm e}^{-h/T}$ and $t = {\rm e}^{-J/T}$ with $h$ denoting an externally applied magnetic field, $T$ the…

There is no an exact solution to three-dimensional (3D) finite-size Ising model (referred to as the Ising model hereafter for simplicity) and even two-dimensional (2D) Ising model with non-zero external field to our knowledge. Here by using…