Ground-state properties of the spin-1/2 antiferromagnetic Heisenberg model on a square lattice by a Monte Carlo method

1994 ◽  
Vol 49 (9) ◽  
pp. 5983-5987 ◽  
Author(s):  
R. A. Sauerwein ◽  
M. J. de Oliveira
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ground State ◽  
Heisenberg Model ◽  
Square Lattice ◽  
Ground State Properties ◽  
Antiferromagnetic Heisenberg Model

GROUND-STATE PROPERTIES OF THE SPIN-1/2 ANTIFERROMAGNETIC HEISENBERG MODEL ON A CUBIC LATTICE BY A MONTE CARLO METHOD

1995 ◽  
Vol 09 (10) ◽  
pp. 619-627 ◽  
Author(s):  
R. A. SAUERWEIN ◽  
M. J. DE OLIVEIRA
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Ground State Energy ◽  
Ground State ◽  
Heisenberg Model ◽  
State Energy ◽  
Isotropic Case ◽  
Spatial Anisotropy ◽  
Cubic Lattice ◽  
Antiferromagnetic Heisenberg Model

The spin-1/2 antiferromagnetic Heisenberg model with spatial anisotropy is studied on a cubic lattice by a Monte Carlo Method. Two types of spatial anisotropies are considered: planar and axial. The staggered magnetization m† and the ground state energy per site ∊0 are obtained as a function of the anisotropy. In the isotropic case we have obtained m† = 0.429 ± 0.001 in units where the saturated value is 0.5 and ∊0 = –0.899 ± 0.001.

Simulation of Thermal Cooling Curves in the Process to Ordering Alloys by the Monte Carlo Method

2021 ◽  
Vol 410 ◽  
pp. 227-234
Author(s):  
Albert R. Khalikov ◽  
Sergey V. Dmitriev
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Stoichiometric Composition ◽  
Square Lattice ◽  
Cooling Curves ◽  
Ordering Kinetics ◽  
The Monte Carlo Method ◽  
Proposed Model ◽  
Coordination Spheres ◽  
Thermal Cooling

An algorithm is proposed for constructing curves of thermal cooling and ordering kinetics with a monotonic decrease in temperature for alloys to stoichiometric composition. Modeling is carried out by the Monte Carlo method in the model of a rigid crystal lattice and pair interatomic interactions. The application of the algorithm is illustrated by the example to a square lattice, taking into account interatomic interactions in the first two coordination spheres for alloys with the composition AB, A3B, and A3B5. The proposed model makes it possible to calculate individual sections of the phase diagrams to the state for binary alloys.

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