Lower bound approximation to the free energy of an Ising model on a simple cubic lattice

1981 ◽  
Vol 59 (10) ◽  
pp. 1291-1295 ◽  
Author(s):  
Chin-Kun Hu ◽  
Wen-Den Chen ◽  
Yu-Ming Shih ◽  
Dong-Chung Jou ◽  
C. K. Pan ◽  
...  
Keyword(s):  
Free Energy ◽  
Ising Model ◽  
Lower Bound ◽  
Variational Method ◽  
Critical Point ◽  
Zero Field ◽  
Free Energies ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

We apply a modified Kadanoff's variational method to calculate the lower bound zero-field free energies and their derivatives for an Ising model on the simple cubic lattice. We find a critical point at Kc = 0.2393769 with precision ±10−7.

scholarly journals The Possibility of Many Compensation Points in a Mixed-Spin Ising Ferrimagnetic System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hadey K. Mohamad
Keyword(s):  
Free Energy ◽  
Mean Field ◽  
Field Approximation ◽  
Spin Model ◽  
Mean Field Approximation ◽  
Zero Field ◽  
Mixed Spin ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
The Mean

The magnetic properties of a ferrimagnetic mixed spin-3/2 and spin-5/2 Ising model with different anisotropies are investigated by using the mean-field approximation (MFA). In particular, the effect of magnetic anisotropies on the compensation phenomenon, acting on A-atoms and B-ones for the mixed-spin model, has been considered in a zero field. The free energy of a mixed-spin Ising ferrimagnetic system from MFA of the Hamiltonian is calculated. By minimizing the free energy, we obtain the equilibrium magnetizations and the compensation points. The phase diagram of the system in the anisotropy dependence of transition temperature has been discussed as well. Our results of this model predict the existence of many (two or three) compensation points in the ordered system on a simple cubic lattice.

scholarly journals Effect of Anisotropy on the Critical Behaviour of Three- Dimensional Heisenberg Ferromagnets

1976 ◽  
Vol 31 (1) ◽  
pp. 34-40 ◽  
Author(s):  
R. Shanker ◽  
R. A. Singh
Keyword(s):  
Three Dimensional ◽  
Experimental Investigations ◽  
Isotropic Case ◽  
Zero Field ◽  
Critical Temperatures ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Anisotropic System ◽  
Critical Temperature Tc

The anisotropic nearest-neighbour Heisenberg model for the simple cubic lattice has been investigated by interpolating the anisotropy between the Ising and isotropic Heisenberg limits via general spin high-temperature series expansions of the zero-field suspectibility. This is done by estimating the critical temperature (Tc(3)) and the susceptibility exponent γ from the analysis of the series by the Ratio and Pade approximants methods. It is noted that Tc(3) varies with anisotropy while γ is almost the same for the anisotropic system, and a jump in it occurs for the isotropic case in agreement with the universality hypothesis. The effect of anisotropy on the susceptibility is also shown. Further, it is seen that estimates of γ for the two extreme limits agree well with those of previous theoretical as well as experimental investigations. In addition, critical temperatures have been summarised in a relation, and expressions for the magnetisation have been derived.

scholarly journals 3D ISING NONUNIVERSALITY: A MONTE CARLO STUDY

2005 ◽  
Vol 16 (08) ◽  
pp. 1217-1224 ◽  
Author(s):  
MELANIE SCHULTE ◽  
CAROLINE DROPE
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
External Field ◽  
Nearest Neighbor ◽  
Monte Carlo Study ◽  
Universality Class ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
Binder Cumulant

We investigate as a member of the Ising universality class the Next-Nearest Neighbor Ising model without external field on a simple cubic lattice by using the Monte Carlo Metropolis Algorithm. The Binder cumulant and the susceptibility ratio, which should be universal quantities at the critical point, were shown to vary for small negative next-nearest neighbor interactions.

scholarly journals Spin Waves and Skyrmions in Magneto-Ferroelectric Superlattices: Theory and Simulation†

Proceedings ◽  
2019 ◽  
Vol 46 (1) ◽  
pp. 3
Author(s):  
Hung Diep ◽  
Ildus Sharafullin
Keyword(s):  
Spin Waves ◽  
Wave Length ◽  
Magnetic Films ◽  
Zero Field ◽  
Ferroelectric Films ◽  
Spin Configuration ◽  
Dm Interaction ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

We present in this paper the effects of Dzyaloshinskii–Moriya (DM) magnetoelectric coupling between ferroelectric and magnetic layers in a superlattice formed by alternate magnetic and ferroelectric films. Magnetic films are films of simple cubic lattice with Heisenberg spins interacting with each other via an exchange J and a DM interaction with the ferroelectric interface. Electrical polarizations of ± 1 are assigned at simple cubic lattice sites in the ferroelectric films. We determine the ground-state (GS) spin configuration in the magnetic film. In zero field, the GS is periodically non-collinear (helical structure) and in an applied field H perpendicular to the layers, it shows the existence of skyrmions at the interface. Using the Green’s function method we study the spin waves (SW) excited in a monolayer and also in a bilayer sandwiched between ferroelectric films, in zero field. We show that the DM interaction strongly affects the long-wave length SW mode. We calculate also the magnetization at low temperatures. We use next Monte Carlo simulations to calculate various physical quantities at finite temperatures such as the critical temperature, the layer magnetization and the layer polarization, as functions of the magneto-electric DM coupling and the applied magnetic field. Phase transition to the disordered phase is studied.

scholarly journals Skyrmions and Spin Waves in Magneto–Ferroelectric Superlattices

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 862
Author(s):  
Ildus F. Sharafullin ◽  
Hung T. Diep
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Triangular Lattice ◽  
Applied Field ◽  
Zero Field ◽  
Ferroelectric Films ◽  
Dm Interaction ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice

We present in this paper the effects of Dzyaloshinskii–Moriya (DM) magneto–electric coupling between ferroelectric and magnetic interface atomic layers in a superlattice formed by alternate magnetic and ferroelectric films. We consider two cases: magnetic and ferroelectric films have the simple cubic lattice and the triangular lattice. In the two cases, magnetic films have Heisenberg spins interacting with each other via an exchange J and a DM interaction with the ferroelectric interface. The electrical polarizations of ±1 are assumed for the ferroelectric films. We determine the ground-state (GS) spin configuration in the magnetic film and study the phase transition in each case. In the simple cubic lattice case, in zero field, the GS is periodically non collinear (helical structure) and in an applied field H perpendicular to the layers, it shows the existence of skyrmions at the interface. Using the Green’s function method we study the spin waves (SW) excited in a monolayer and also in a bilayer sandwiched between ferroelectric films, in zero field. We show that the DM interaction strongly affects the long-wave length SW mode. We calculate also the magnetization at low temperatures. We use next Monte Carlo simulations to calculate various physical quantities at finite temperatures such as the critical temperature, the layer magnetization and the layer polarization, as functions of the magneto–electric DM coupling and the applied magnetic field. Phase transition to the disordered phase is studied. In the case of the triangular lattice, we show the formation of skyrmions even in zero field and a skyrmion crystal in an applied field when the interface coupling between the ferroelectric film and the ferromagnetic film is rather strong. The skyrmion crystal is stable in a large region of the external magnetic field. The phase transition is studied.

Critical 2D and 3D Dynamics of Q2R Cellular Automata

1997 ◽  
Vol 08 (06) ◽  
pp. 1263-1266 ◽  
Author(s):  
D. Stauffer
Keyword(s):  
Ising Model ◽  
Cellular Automata ◽  
Square Lattice ◽  
Cubic Lattice ◽  
Simple Cubic ◽  
Simple Cubic Lattice ◽  
2D And 3D

Simulation of critical relaxation of the magnetization in a microcanonical Ising model agrees with the expected exponent z ≃2 after very long times on the square lattice, while on the simple cubic lattice z≃3.3 seems different.

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