Related papers: Ansatz for the Two-Dimensional Ising Model in an E…
In this paper a new approach to solving the 2D and 3D Ising models in external magnetic field $H\neq0$ is developed. The general formalism for the approach to the problem is presented on the example of the 2D Ising model in the external…
The two-dimensional Ising model is the simplest model of statistical mechanics exhibiting a second order phase transition. While in absence of magnetic field it is known to be solvable on the lattice since Onsager's work of the forties,…
The exact solution of the two-dimensional (2D) Ising model at an external magnetic field is derived by a modified Clifford algebraic approach. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic…
The partition functions for two-dimensional nearest neighbour Ising model in a non-zero magnetic field have been derived for finite square lattices with the help of graph theoretical procedures, show-bit algorithm, enumeration of…
We conjecture an approximate expression for the free energy in the thermodynamic limit of the classical square lattice Ising model in a uniform (real) magnetic field. The zero-field result is well known due to Onsager for more than eighty…
We study some properties of the Ising model in the plane of the complex (energy/temperature)-dependent variable $u=e^{-4K}$, where $K=J/(k_BT)$, for nonzero external magnetic field, $H$. Exact results are given for the phase diagram in the…
There is no an accepted exact partition function (PF) for the two-dimensional (2D) Ising model with a non-zero external magnetic field to our knowledge. Here we infer an empirical PF for such an Ising model. We compare the PFs for two…
We revisit the problem of spontaneous magnetization of the one-dimensional Ising model from the Landau free energy perspective. To this end, we define and calculate the density of states of the one-dimensional Ising model following a…
We suggest the new definition of the magnetization. For the two - dimensional Ising model with the free boundary conditions we calculate any derivative of this magnetization for zero magnetic field.
For temperatures below the critical temperature, the magnetic susceptibility for the two-dimensional isotropic Ising model can be expressed in terms of an infinite series of multiple integrals. With respect to a parameter related to…
The one-dimensional Ising model in an external magnetic field with uniform long-range interactions and random short-range interactions satisfying bimodal annealed distributions is studied. This generalizes the random model discussed by…
In this case study, we illustrate the great potential of experimental mathematics and symbolic computation, by rederiving, ab initio, Onsager's celebrated solution of the twodimensional Ising model in zero magnetic field. Onsager's…
We investigate the ground state and the thermal entanglement in the two-qubit Ising model interacting with a site-dependent magnetic field. The degree of entanglement is measured by calculating the concurrence. For zero temperature and for…
The partition function and magnetization equations are derived for the two-dimensional nearest neighbour Ising models in a magnetic field.
We suggest the new definition of the magnetization. For the two - dimensional Ising model with the free boundary conditions we calculate this magnetization.
In this paper a new approach to solving the Ising-Onsager problem in external magnetic field is investigated. The expression for free energy on one Ising spin in external field both for the twodimensional and threedimensional Ising model…
We study the complex-temperature properties of a rare example of a statistical mechanical model which is exactly solvable in an external symmetry-breaking field, namely, the Ising model on the square lattice with $\beta H = \pm i \pi/2$.…
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…
We report tests of finite-size scaling ansatzes in the low temperature phase of the two-dimensional Ising model. For moments of the magnetisation density, we find good agreement with the new ansatz of Borgs and Koteck\'y, and clear evi…
We study random field Ising model on $\mathbb Z^2$ where the external field is given by i.i.d.\ Gaussian variables with mean zero and positive variance. We show that at zero temperature the effect of boundary conditions on the magnetization…