Related papers: n-vicinity method for Ising Model with long-range …
In a previous work, the n-vicinity method for approximate calculation of the partition function of a spin system was proposed. The equation of state was obtained in the most general form. In the present paper, we analyze the applicability…
We use an m-vicinity method to examine Ising models on hypercube lattices of high dimensions d>=3. This method is applicable for both short-range and long-range interactions. We introduce a small parameter, which determines whether the…
In many applications of spin models, the fast estimation of their critical temperatures and other physical properties is of great importance. In this work, we present the analytical expressions estimating the critical properties of…
Recently, it has been found that an effective long-range interaction is realized among local bistable variables (spins) in systems where the elastic interaction causes ordering of the spins. In such systems, generally we expect both…
The n-vicinities method for approximate calculations of the partition function of a spin system was proposed previously. The equation of state was obtained in the most general form. In the present publication these results are adapted to…
We study the Ising model on $\mathbb{Z}^{2}$ and show, via numerical simulation, that allowing interactions between spins separated by distances $1$ and $m$ (two ranges), the critical temperature, $ T_c (m) $, converges monotonically to the…
The large amounts of data from molecular biology and neuroscience have lead to a renewed interest in the inverse Ising problem: how to reconstruct parameters of the Ising model (couplings between spins and external fields) from a number of…
We investigate a two-dimensional Ising model with long-range interactions that emerge from a generalization of the magnetic dipolar interaction in spin systems with in-plane spin orientation. This interaction is, in general, anisotropic…
We present a generalized expression for the transfer matrix of finite and infinite one-dimensional spin chains within a magnetic field with spin pair interaction $J/r^p$, where $r\ = 1,2,\ldots,n_v$ is the distance between two spins, $n_v$…
Effective interactions that violate Newton's third law of action-reaction symmetry are common in systems where interactions are mediated by a non-equilibrium environment. Extensive Monte Carlo simulations are carried out on a…
We consider a model for thermal contact through a diathermal interface between two macroscopic bodies at different temperatures: an Ising spin chain with nearest neighbor interactions is endowed with a Glauber dynamics with different…
A new method for locating analytically critical temperatures is discussed. It is exact for selfdual systems. When applied the two coupled layers of Ising spins it deviates from our preliminary Monte Carlo estimates by 1.5 standard…
For a 1D Ising model, we obtained an exact expression for the spectral density in an n-vicinity of the ground state and explained why our n-vicinity method with the Gaussian approximation of the spectral density did not applicable in this…
A field-theoretic description of critical behavior of Ising systems with long-range interactions is obtained in the two-loop approximation directly in the three-dimensional space. It is shown that long-range interactions affect the…
An improved unified formulation based on the effective field theory is introduced for a spin-1/2 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the…
The dynamics of the spins in the Ising model are analyzed using a virtual walk scenario. The system is quenched from a very high temperature to a lower one using the Glauber scheme in one and two dimensions. A walk is associated with each…
We demonstrate the applicability of the $\epsilon$-convergence algorithm in extracting the critical temperatures and critical exponents of three-dimensional Ising models. We analyze the low temperature magnetization as well as high…
A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. Low-temperature properties of this model are investigated. The susceptibility and the specific heat are…
We present a numerical study to determine nucleation rates for magnetisation reversal within the Ising model (lattice gas model) in the low-temperature regime, a domain less explored in previous research. To achieve this, we implemented the…
We construct and analyse a dual model to the Ising model with the nearest and next-nearest neighbors on the rectangular lattice (NNNI model). The Hamiltonian of the dual model turns out to contain two- and four-spin interactions. The free…