Related papers: Relevant spontaneous magnetization relations for t…
The equations for the spontaneous magnetization for different three-dimensional lattices have been derived in a heuristic manner. The estimated critical temperatures for simple cubic, face-centered cubic, body-centered cubic and diamond…
The correlation functions and spontaneous magnetization are calculated for the three-dimensional Ising model and for the three-dimensional Z_2 electrodynamics.
The relevant approximate spontaneous magnetization relations for the simple-cubic and body-centered-cubic Ising lattices have recently been obtained analytically by a novel approach that conflates the Callen--Suzuki identity with a…
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,…
The spontaneous magnetization of the Kagome lattice in the Ising model is investigated. The proof of the fallacy of spontaneous magnetization obtained earlier and repeatedly migrating from publication to publication is given. An exact…
Recently we have performed large-scale average magnetization studies of the Ising model for the square, honeycomb, triangular, and simple cubic lattice. We want to complement those studies with the structurally more complicated…
A simple, general and practically exact method is developed for the equilibrium properties of the macroscopic physical systems with translational symmetry. Applied to the Ising model in two and three dimension, a modest calculation gives…
The magnetization dynamics of the triangular lattice of Ising spin chains is investigated in the framework of a two-dimensional model. The rigid chains are assumed to interact with the nearest neighboring chains, an external magnetic field,…
The spontaneous magnetization is proved to vanish continuously at the critical temperature for a class of ferromagnetic Ising spin systems which includes the nearest neighbor ferromagnetic Ising spin model on $\mathbb Z^d$ in $d=3$…
In this work, we study the magnetization behaviors of the classical Ising model on the triangular lattice using Monte Carlo simulations, and pay particular attention to the effect of further-neighbor interactions. Several fascinating spin…
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…
We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we…
A systematic study of both classical and quantum geometric frustrated Ising models with a competing ordering mechanism is reported in this paper. The ordering comes in the classical case from a coupling of 2D layers and in the quantum model…
Using Cellular Automata, we simulate spin systems corresponding to $2d$ Ising model with various kinds of boundary conditions (bcs). The appearance of spontaneous magnetization in the absence of magnetic field is studied with a $64\times64$…
We report the conjectures on the three-dimensional (3D) Ising model on simple orthorhombic lattices, together with the details of calculations for a putative exact solution. Two conjectures, an additional rotation in the fourth curled-up…
Using zero temperature Monte Carlo simulations we have studied the magnetic hysteresis in a three-dimensional Ising model with nearest neighbor exchange and dipolar interaction. The average magnetization of spins located inside a sphere on…
The partition function and magnetization equations are derived for the two-dimensional nearest neighbour Ising models in a magnetic field.
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…
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…
Lars Onsager announced in 1949 that he and Bruria Kaufman had proved a simple formula for the spontaneous magnetization of the square-lattice Ising model, but did not publish their derivation. It was three years later when C. N. Yang…