相关论文: Monotonicity of Ursell functions in the Ising mode…
Ursell functions $U_n$ are higher-order generalizations of the covariance function, which capture the interactions between $n$ random variables. In the classical Ising model, as shown by Shlosman, when considering the spins at some…
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…
The correlation function of two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor representation are…
We consider the zeros of the partition function of the Ising model with ferromagnetic pair interactions and complex external field. Under the assumption that the graph with strictly positive interactions is connected, we vary the…
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…
Using a combinatorial method, the partition functions for two-dimensional nearest neighbour Ising models have been derived for a square lattice of 16 sites in the presence of the magnetic field. A novel hierarchical method of enumeration of…
For a grand canonical ensemble of classical point-like particles at equilibrium in continuous space we investigate the functional relationship between a stable and regular pair potential describing the interaction of the particles and the…
The partition function and magnetization equations are derived for the two-dimensional nearest neighbour Ising models in a magnetic field.
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…
The Ising model, in presence of an external magnetic field, is isomorphic to a model of localized interacting particles satisfying the Fermi statistics. By using this isomorphism, we construct a general solution of the Ising model which…
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 a system of galaxies in gravitational interaction can be cast in an Ising Model form, and this reformulated via a Hubbard--Stratonovich transformation into a three dimensional stochastic and classical scalar field…
We rigorously derive the Ornstein-Zernike asymptotics of the pair-correlation functions for finite-range Ising ferromagnets in any dimensions and at any temperature above critical.
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…
The bulk and boundary magnetizations are calculated for the critical Ising model on a randomly triangulated disk in the presence of a boundary magnetic field h. In the continuum limit this model corresponds to a c = 1/2 conformal field…
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 consider two bidimensional classical Ising models, coupled by a weak interaction bilinear in the energy densities of the two systems; the model contains, as limiting cases, the Ashkin-Teller and the Eight-vertex models for certain values…
We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins), separated by a distance $\ell$, decay, on average, faster…
Let $X = \{1,-1\}^\mathbb{N}$ be the symbolic space endowed with the product order. A Borel probability measure $\mu$ over $X$ is said to satisfy the FKG inequality if for any pair of continuous increasing functions $f$ and $g$ we have…
The correlation function of the two dimensional Ising model with the nearest neighbours interaction on the finite size lattice with the periodical boundary conditions is derived. The expressions similar to the form factor expansion are…