Related papers: Exact solution of the two-dimensional (2D) Ising m…
The exact solution of a two-dimensional (2D) Ising model with the next nearest interactions at zero magnetic field is derived. At first, the transfer matrices are analyzed in three representations, i.e., Clifford algebraic representation,…
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…
There is no an exact solution to three-dimensional (3D) finite-size Ising model (referred to as the Ising model hereafter for simplicity) and even two-dimensional (2D) Ising model with non-zero external field to our knowledge. Here by using…
The exact solution of ferromagnetic two-dimensional (2D) Ising model with a transverse field, which can be used to describe the critical phenomena in low-dimensional quantum spin systems, is derived by equivalence between the ferromagnetic…
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…
The three-dimensional (3D) Ising model is mapped into a 3D spinless fermionic model by the Jordan-Wigner transformation. The exact solution of the 3D model for spinless fermions is derived analytically by performing a diagonalization…
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,…
Three-dimensional Ising model in zero external field is exactly solved by operator algebras, similar to the Onsager's approach in two dimensions. The partition function of the simple cubic crystal imposed by the periodic boundary condition…
We study dimensional crossover in Ising systems at complex temperatures by comparing three types of system: the infinite isotropic 2D Ising model; the infinite anisotropic 2D Ising model; and Ising ladders with a finite number of legs. In…
The use of a transfer matrix method to solve the 3D Ising model is straightforwardly generalized from the 2D case. We follow B.Kaufman's approach. No approximation is made, however the largest eigenvalue cannot be identified. This problem…
An overview of the mathematical structure of the three-dimensional (3D) Ising model is given, from the viewpoints of topologic, algebraic and geometric aspects. By analyzing the relations among transfer matrices of the 3D Ising model,…
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…
In this work, we first focus on the mathematical structure of the three-dimensional (3D) Ising model. In the Clifford algebraic representation, many internal factors exist in the transfer matrices of the 3D Ising model, which are ascribed…
The Ising model on an alternating triangular lattice with the nearest-neighbor interaction in a magnetic field is presented. Exact solution of this model is found. The thermodynamic quantities, like free energy, specific heat a finite…
We present an exact analytical solution for the one-dimensional Ising model in the presence of an external magnetic field applied periodically to every $k$-th site. The problem is handled using the symmetrized transfer matrix approach, we…
The site-decorated Ising model is introduced to advance the understanding and experimental realization of the recently discovered one-dimensional (1D) finite-temperature ultranarrow phase crossover in an external magnetic field, while…
We study the finite size corrections for the magnetization and the internal energy of the 2d Ising model in a magnetic field by using transfer matrix techniques. We compare these corrections with the functional form recently proposed by…
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…
We obtain the exact physical characteristics of the triple-chain Ising model on a torus with all possible multispin interactions invariant with respect to rotation by the angle $2\pi / 3$. The exact value of the partition function in a…
We develop a Clifford algebra approach for 3D Ising model. By utilizing some mathematical facts of the direct product of matrices and their trace, we expand the dimension of the transfer matrices V of the 3D Ising system by adding unit…