Frustrations and Phase Transitions in Ising Model on 2D Lattices

2010 ◽  
Vol 168-169 ◽  
pp. 435-438 ◽  
Author(s):  
Felix A. Kassan-Ogly ◽  
B.N. Filippov ◽  
V.V. Men’shenin ◽  
Akai K. Murtazaev ◽  
M.K. Ramazanov ◽  
...  
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Method ◽  
Ising Model ◽  
Analytical Solutions ◽  
Nearest Neighbors ◽  
Square Lattice ◽  
Maximum Eigenvalue ◽  
Exact Analytical Solutions

The problem of frustrations and phase transition appearance or suppression is studied on the base of exact analytical solutions for maximum eigenvalue of Kramers-Wannier transfer matrix in the Ising model on a square lattice [1], a triangular and honeycomb lattices [2], and kagome lattice [3] with allowance for the interactions between nearest J is studied. We also studied these phenomena by the numerical “replica Monte Carlo method”, taking also into account the interactions between next-nearest neighbors J'.

Monte Carlo Modelling of Phase Transitions in Quasi-One-Dimensional Multiferoic

2016 ◽  
Vol 845 ◽  
pp. 158-161
Author(s):  
S.J. Lamekhov ◽  
Dmitry A. Kuzmin ◽  
Igor V. Bychkov ◽  
I.A. Maltsev ◽  
V.G. Shavrov
Keyword(s):  
Magnetic Field ◽  
Phase Transition ◽  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Method ◽  
External Magnetic Field ◽  
Periodic Potential ◽  
One Dimensional ◽  
Field Modelling ◽  
Energy Components

Behavior of quasi-one-dimensional multiferoic Ca3CoMnO6 in external magnetic field was investigated. Modelling by Monte Carlo method was performed to show influence of external magnetic field on appearance of polarization and temperature of phase transition in electric subsystem. Magnetization, polarization and energy components for magnetic and electric subsystems dependencies were achieved for different values of external magnetic field. Modelling showed that periodic potential in form of Frenkel-Kontorova makes influence on maximal values and temperature of phase transitions for magnetization and polarization.

Magnetic Concentration Phase Transitions in Ultrathin Films

2013 ◽  
Vol 683 ◽  
pp. 69-72 ◽  
Author(s):  
Leonid Afremov ◽  
Ilia Ilyushin
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Ising Model ◽  
Curie Temperature ◽  
Percolation Threshold ◽  
Ultrathin Films ◽  
Magnetic State ◽  
Critical Concentration ◽  
Magnetic Moments ◽  
Nearest Neighbors

Modeling study of magnetic and concentration phase transition in ultrathin films of diluted magnet has been carried out under approximation of random interaction between atomic magnetic moments of nearest neighbors and within the framework of Ising model. The dependence of Curie temperature on concentration of magnetic atoms was formed. It is shown that with increasing of thickness of ultrathin film the critical concentration of transition from unordered to ordered magnetic state decreases down to the value equal to the percolation threshold.

The Investigation of Phase Transitions in Two-Dimensional 3-State Antiferromagnetic Potts Model on a Triangular Lattice with Interaction of Next Nearest Neighbors

2014 ◽  
Vol 215 ◽  
pp. 52-54 ◽  
Author(s):  
Akai K. Murtazaev ◽  
A.B. Babaev ◽  
Felix A. Kassan-Ogly
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Method ◽  
Potts Model ◽  
Triangular Lattice ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Two Dimensional ◽  
Critical Temperatures ◽  
Antiferromagnetic Potts Model

The phase transitions and critical phenomena in two-dimensional 3-state antiferromagnetic Potts model with account of next-nearest neighbors are investigated by Monte-Carlo method. The systems with linear sizesL=20-144 are explored. Following parities of exchange interactions are considered. Moreover, we analyze the character of phase transitions and determine the critical temperatures.

scholarly journals MONTE-CARLO SIMULATIONS OF PHASE TRANSITIONS IN THE TWO-DIMENSIONAL ISING MODEL WITH LONG-RANGE CORRELATIONS

2017 ◽  
Vol 18 (9) ◽  
pp. 159-163
Author(s):  
A.A. Biryukov ◽  
Y.V. Degtyareva ◽  
M.A. Shleenkov
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Critical Temperature ◽  
Monte Carlo Method ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Long Range ◽  
Temperature Increase ◽  
Two Dimensional ◽  
Long Range Correlations

In this article phase transitions in the modified two-dimensional Ising model with long-range correlations investigated. This model was studied with Monte-Carlo method and Metropolis algorithm. Critical temperature increase is shown in such model.

Phase Transition Determinated by Weighted Monte Carlo Simulations

2012 ◽  
Vol 268-270 ◽  
pp. 1158-1162
Author(s):  
Qing Xin Yuan ◽  
Zhan Wei Wang ◽  
Yin Xiao Du ◽  
Fan Guang Zeng
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Monte Carlo ◽  
Phase Transitions ◽  
Monte Carlo Method ◽  
Monte Carlo Simulations ◽  
Critical Values ◽  
Monte Carlo Procedure

We study the weighted Monte Carlo method, which was proposed by Milchev, Heermann and Binder. First, we describe our method and the Monte Carlo procedure. Second, we apply the procedure to study the phase transitions of and Sine-Gordon models, respectively. The critical values of the parameters allow us to determine the phase diagram of the models.

Monte Carlo study of phase transitions in an Ising model superlattice

1991 ◽  
Vol 69 (8) ◽  
pp. 6158-6160 ◽  
Author(s):  
Jialin Li ◽  
D. P. Landau
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Ising Model ◽  
Monte Carlo Study

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.

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cellular Automaton ◽  
Intermediate Phase ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

Concentration Phase Transition in a Two-Dimensional Ferromagnet

2020 ◽  
Vol 312 ◽  
pp. 244-250
Author(s):  
Alexander Konstantinovich Chepak ◽  
Leonid Lazarevich Afremov ◽  
Alexander Yuryevich Mironenko
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Thermal Effect ◽  
Spin State ◽  
Critical Concentration ◽  
Two Dimensional ◽  
Percolation Transition ◽  
Magnetic Cluster ◽  
The Monte Carlo Method

The concentration phase transition (CPT) in a two-dimensional ferromagnet was simulated by the Monte Carlo method. The description of the CPT was carried out using various order parameters (OP): magnetic, cluster, and percolation. For comparison with the problem of the geometric (percolation) phase transition, the thermal effect on the spin state was excluded, and thus, CPT was reduced to percolation transition. For each OP, the values ​​of the critical concentration and critical indices of the CPT are calculated.

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