Related papers: Partition Function of the Ising Model via Factor G…
Normal factor graph duality offers new possibilities for Monte Carlo algorithms in graphical models. Specifically, we consider the problem of estimating the partition function of the ferromagnetic Ising and Potts models by Monte Carlo…
We propose Monte Carlo methods to estimate the partition function of the two-dimensional Ising model in the presence of an external magnetic field. The estimation is done in the dual of the Forney factor graph representing the model. The…
Algebraic topology studies topological spaces with the help of tools from abstract algebra. The main focus of this paper is to show that many concepts from algebraic topology can be conveniently expressed in terms of (normal) factor graphs.…
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 give a Pfaffian formula to compute the partition function of the Ising model on any graph $G$ embedded in a closed, possibly non-orientable surface. This formula, which is suitable for computational purposes, is based on the relation…
The dual normal factor graph and the factor graph duality theorem have been considered for discrete graphical models. In this paper, we show an application of the factor graph duality theorem to continuous graphical models. Specifically, we…
In this paper, we show analytically that the duality of normal factor graphs (NFG) can facilitate stochastic estimation of partition functions. In particular, our analysis suggests that for the $q-$ary two-dimensional nearest-neighbor Potts…
The partition function for two-dimensional nearest neighbour Ising models in the presence of a magnetic field is derived . A comparison with the partition functions predicted by Onsager is carried out. The critical temperature estimated by…
Graphical models represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function, is the main inference challenge relevant to multiple statistical and…
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…
Although symmetry methods and analysis are a necessary ingredient in every physicist's toolkit, rather less use has been made of combinatorial methods. One exception is in the realm of Statistical Physics, where the calculation of the…
The partition functions of ferromagnetic Ising models of square lattices in a finite magnetic field is deduced using topological considerations within a heuristic graph-theoretical approach. These equations are derived separately for low…
Employing heuristic susceptibility equations in conjunction with the well-known critical exponents, the magnetization and partition function for two-dimensional nearest neighbour Ising models are formulated in terms of the Gauss…
The exact partition function of the two-dimensional nearest neighbour Ising model pertaining to square lattices is derived for N sites in the case of a non-vanishing magnetic field.When the magnetic field is zero,the partition functions…
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…
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…
The partition function of two-dimensional nearest neighbour Ising models in a non-zero magnetic field is derived employing a matrix formulation.
We design a recursive algorithm to compute the partition function of the Ising model, summed over cubic maps with fixed size and genus. The algorithm runs in polynomial time, which is much faster than methods based on a Tutte-like, or…
We propose an importance sampling scheme to estimate the partition function of the two-dimensional ferromagnetic Ising model and the two-dimensional ferromagnetic $q$-state Potts model, both in the presence of an external magnetic field.…
An integral representation of the partition function for general $n$-dimensional Ising models with nearest or non-nearest neighbours interactions is given. The representation is used to derive some properties of the partition function. An…