Phase Transformations and Thermodynamic Properties of the Potts Model with q = 4 on a Hexagonal Lattice with Interactions of Next-Nearest Neighbors

2020 ◽  
Vol 62 (3) ◽  
pp. 499-503 ◽  
Author(s):  
M. K. Ramazanov ◽  
A. K. Murtazaev ◽  
M. A. Magomedov ◽  
M. K. Mazagaeva
Keyword(s):  
Thermodynamic Properties ◽  
Phase Transformations ◽  
Potts Model ◽  
Hexagonal Lattice ◽  
Nearest Neighbors

Computer simulation of the Potts model with the number of spin states q = 4 on a triangular lattice

2020 ◽  
pp. 57-64
Author(s):  
Magomedsheikh Ramazanov ◽  
Akai Murtazaev
Keyword(s):  
Computer Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermodynamic Properties ◽  
Potts Model ◽  
Triangular Lattice ◽  
Nearest Neighbors ◽  
Spin States ◽  
Two Dimensional ◽  
The Monte Carlo Method

Based on the Wang-Landau algorithm, the Monte Carlo method is used to study the thermodynamic properties of the two-dimensional Potts model with the number of spin states $q=4$ on a triangular lattice, taking into account the interactions of the first and second nearest neighbors. It is shown that taking into account antiferromagnetic interactions of the second nearest neighbors leads to frustration.

Phase Diagram of the Antiferromagnetic Potts Model with Number q = 4 of Spin States in the Hexagonal Lattice

2021 ◽  
Vol 122 (5) ◽  
pp. 428-433
Author(s):  
A. K. Murtazaev ◽  
M. K. Mazagaeva ◽  
M. K. Ramazanov ◽  
M. A. Magomedov
Keyword(s):  
Phase Diagram ◽  
Potts Model ◽  
Hexagonal Lattice ◽  
Spin States ◽  
Antiferromagnetic Potts Model

scholarly journals ON INHOMOGENEOUS p-ADIC POTTS MODEL ON A CAYLEY TREE

2005 ◽  
Vol 08 (02) ◽  
pp. 277-290 ◽  
Author(s):  
FARRUKH MUKHAMEDOV ◽  
UTKIR ROZIKOV
Keyword(s):  
Gibbs Measure ◽  
Potts Model ◽  
Cayley Tree ◽  
Nearest Neighbor ◽  
Gibbs Measures ◽  
Nearest Neighbors ◽  
Translation Invariant

We consider a nearest-neighbor inhomogeneous p-adic Potts (with q≥2 spin values) model on the Cayley tree of order k≥1. The inhomogeneity means that the interaction Jxy couplings depend on nearest-neighbors points x, y of the Cayley tree. We study (p-adic) Gibbs measures of the model. We show that (i) if q∉pℕ then there is unique Gibbs measure for any k≥1 and ∀ Jxy with | Jxy |< p-1/(p -1). (ii) For q∈p ℕ, p≥3 one can choose Jxy and k≥1 such that there exist at least two Gibbs measures which are translation-invariant.

Application of Statistical Moment Method to Thermodynamic Properties and Phase Transformations of Metals and Alloys

2008 ◽  
Vol 138 ◽  
pp. 209-240 ◽  
Author(s):  
K. Masuda-Jindo ◽  
Vu Van Hung ◽  
P.E.A. Turchi
Keyword(s):  
Thermodynamic Properties ◽  
Phase Transformations ◽  
Moment Method ◽  
Structural Phase ◽  
Equilibrium Phase ◽  
Statistical Moment ◽  
Metals And Alloys ◽  
Thermodynamic Quantities ◽  
Specific Heats ◽  
Statistical Moment Method

The thermodynamic properties and phase transformations of metals and alloys are studied using the statistical moment method, going beyond the quasi-harmonic approximations. Including the power moments of the atomic displacements up to the fourth order, the Helmholtz free energies and the related thermodynamic quantities are derived explicitly in closed analytic forms. The thermodynamic quantities, like thermal lattice expansion coefficients, specific heats, Grüneisen constants, elastic constants calculated by using the SMM are compared with those of other theoretical schemes and the experimental results. The hcp-bcc structural phase transformations observed for IVB elements, Ti, Zr and Hf, are discussed in terms of the anharmonicity of thermal lattice vibrations. The equilibrium phase diagrams are calculated for the refractory Ta-W and Mo-Ta bcc alloys. In addition, the temperature dependence of the elastic moduli C11, C12 and C14 and those of the ideal tensile and shear strengths of the bcc elements Mo, Ta and W are studied: We also discuss the melting transitions of metals and alloys within the framework of the SMM and estimate the melting temperatures through the limiting temperature of the crystalline stability.

scholarly journals Исследование фазовых переходов и термодинамических свойств модели Поттса с C-=SUB=-q-=/SUB=-=4 на гексагональной решетке с взаимодействиями вторых ближайших соседей

2020 ◽  
Vol 62 (3) ◽  
pp. 442
Author(s):  
М.К. Рамазанов ◽  
А.К. Муртазаев ◽  
М.А. Магомедов ◽  
М.К. Мазагаева
Keyword(s):  
Phase Transitions ◽  
Hexagonal Lattice ◽  
Magnetic Ordering ◽  
Nearest Neighbors ◽  
Magnetic Structures ◽  
First Order ◽  
The Monte Carlo Method ◽  
Cumulant Method ◽  
First Order Transition ◽  
Fourth Order Cumulant

Magnetic structures of the ground state, phase transitions and thermodynamic properties of the 2D ferromagnetic Potts model with the number of spin states q = 4 on a hexagonal lattice with next-nearest neighbors interactions are investigated by the Monte Carlo method based on the Wang-Landau algorithm. It is shown that taking into account the antiferromagnetic interactions of the next-nearest neighbors leads to the appearance of frustration and a violation of magnetic ordering. The orders of the phase transitions are investigated using the Binder fourth-order cumulant method and histogram analysis of data. It is established that a first-order transition is observed in the model being investigated.

Lattice Statics of a Hydrogen Centre in Magnesium

1985 ◽  
Vol 40 (5) ◽  
pp. 439-449
Author(s):  
B. Bratschek ◽  
B. Rager ◽  
H.-J. Volkert
Keyword(s):  
Hydrogen Atom ◽  
Hexagonal Lattice ◽  
Harmonic Approximation ◽  
Nearest Neighbors ◽  
Interstitial Site ◽  
Force Constants ◽  
Ideal Lattice ◽  
Lattice Statics ◽  
Tetrahedral Interstitial Site ◽  
The Ideal

In this work we consider the static perturbation of the hexagonal lattice of magnesium by one stored hydrogen atom. Equations are given to evaluate the equilibrium positions of the ions in the disturbed crystal. The effect of the hydrogen atom is described by a so-called Kanzaki force, an additional force in the ideal lattice. The force between two ions of the ideal lattice is assumed to obey the harmonic approximation. The force constants are calculated form an effective ion-ion potential. The static Green tensor, which is the inverse of the tensor of force constants, is calculated and with its aid the equations of lattice statics are transformed. The transformed equations are solved under the assumption of a Kanzaki force acting only upon the nearest and next-nearest neighbors of the hydrogen atom at a tetrahedral interstitial site. Finally we calculate the volume change Δ V and compare the result with the experimental value.

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