相关论文: Bell polynomials in the series expansions of the I…
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact…
We have substantially extended the high-temperature and low-magnetic-field (and the related low-temperature and high-magnetic-field) bivariate expansions of the free energy for the conventional three-dimensional Ising model and for a…
We derive a closed-form combinatorial expression for the number of states in canonical systems with discrete energy levels. The expression results from the exact low-temperature power series expansion of the partition function. The approach…
The energetic properties of nuclear clusters inside a low-density, finite-temperature medium are studied with a Lattice Gas Model including isospin dependence and Coulomb forces. Important deviations are observed respect to the Fisher…
We propose an algorithm to obtain numerically approximate solutions of the direct Ising problem, that is, to compute the free energy and the equilibrium observables of spin systems with arbitrary two-spin interactions. To this purpose we…
High-temperature expansions are presently the only viable approach to the numerical calculation of the higher susceptibilities for the spin and the scalar-field models on high-dimensional lattices. The critical amplitudes of these…
The new algorithm of the finite lattice method is applied to generate the high-temperature expansion series of the simple cubic Ising model to $\beta^{50}$ for the free energy, to $\beta^{32}$ for the magnetic susceptibility and to…
We derive and analyze the low-activity and low-density expansions of the pressure for the model of a hard-sphere gas on cubic lattices of general dimension $d$, through the 13th order. These calculations are based on our recent extension to…
New algorithm of the finite lattice method is presented to generate the high-temperature expansion series of the Ising model. It enables us to obtain much longer series in three dimensions when compared not only to the previous algorithm of…
We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman's spinor method to calculate low-temperature series expansions for the partition function to high order. From these we can obtain…
Statistical systems on random networks can be formulated in terms of partition functions expressed with integrals by regarding Feynman diagrams as random networks. We consider the cases of random networks with bounded but generic degrees of…
The problem of N interacting spins on a lattice is equivalent to one of N clusters linked in a specific manner. The energy of any configuration of spins can be expressed in terms of the energy levels of this cluster. A new expression is…
Low-temperature expansion of Ising model has long been a topic of significant interest in condensed matter and statistical physics. In this paper we present new results of the coefficients in the low-temperature series of the Ising…
The bond-propagation (BP) algorithm for the specific heat of the two dimensional Ising model is developed and that for the internal energy is completed. Using these algorithms, we study the critical internal energy and specific heat of the…
The paper presents the low temperature expansion of the 2D Ising model in the presence of the magnetic field in powers of $x=\exp(-J/(kT))$ and $z=\exp(B/(kT))$ with full polynomials in $z$ up to $x^{88}$ and full polynomials in $x^4$ up to…
We propose a new algorithm of the finite lattice method to generate the high-temperature series for the Ising model in three dimensions. It enables us to extend the series for the free energy of the simple cubic lattice from the previous…
Using exact results, we determine the complex-temperature phase diagrams of the 2D Ising model on three regular heteropolygonal lattices, $(3 \cdot 6 \cdot 3 \cdot 6)$ (kagom\'{e}), $(3 \cdot 12^2)$, and $(4 \cdot 8^2)$ (bathroom tile),…
We compute the finite-size corrections to the free energy, internal energy and specific heat of the critical two-dimensional spin-1/2 Ising model on a triangular and hexagonal lattices wrapped on a torus. We find the general form of the…
Graphical models for finite-dimensional spin glasses and real-world combinatorial optimization and satisfaction problems usually have an abundant number of short loops. The cluster variation method and its extension, the region graph…
We develop strong-coupling series expansion methods to study two-particle spectra of quantum lattice models. At the heart of the method lies the calculation of an effective Hamiltonian in the two-particle subspace. We explicitly consider an…