Computer Simulation of Critical Behavior of Two-Dimensional Weakly Diluted Antiferromagnetic Potts Model on a Triangular Lattice

2018 ◽  
Vol 60 (6) ◽  
pp. 1180-1183 ◽  
Author(s):  
A. B. Babaev ◽  
A. K. Murtazaev ◽  
G. Ya. Ataeva ◽  
T. R. Rizvanova ◽  
M. R. Dzhamaludinov
Keyword(s):  
Computer Simulation ◽  
Critical Behavior ◽  
Potts Model ◽  
Triangular Lattice ◽  
Two Dimensional ◽  
Antiferromagnetic Potts Model

Influence of Quenched Nonmagnetic Impurities on Phase Transitions in Two-Dimensional 3-State Antiferromagnetic Potts Model on Triangular Lattice

2015 ◽  
Vol 233-234 ◽  
pp. 79-81 ◽  
Author(s):  
A.B. Babaev ◽  
A.K. Murtazaev ◽  
Rashid A. Murtazaliev
Keyword(s):  
Phase Transitions ◽  
Potts Model ◽  
Triangular Lattice ◽  
Two Dimensional ◽  
Nonmagnetic Impurities ◽  
First Order Phase Transition ◽  
The Monte Carlo Method ◽  
Antiferromagnetic Potts Model ◽  
Binder Cumulant ◽  
First Order Phase

An influence of quenched nonmagnetic disorder on the phase transitions in the two dimensional antiferromagnetic Potts model with a number of spin state q=3 on a triangular lattice is calculated by the Monte-Carlo method. The systems with linear sizes L=20÷144 at spin concentrations p=1.00, 0.90, 0.80 are studied. By means of the fourth order Binder cumulant method, the inclusion of a quenched disorder as nonmagnetic impurities into a pure antiferromagnetic Potts model is shown to be the cause of the change of the first order phase transition into the second one.

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.

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.

Topological rearrangements and flow simulation of dry ordered foams

2014 ◽  
Vol 05 (supp01) ◽  
pp. 1441007 ◽  
Author(s):  
J. S. Espinoza Ortiz ◽  
H. Belich ◽  
M. T. D. Orlando ◽  
R. E. Lagos
Keyword(s):  
Strain Rate ◽  
Critical Behavior ◽  
Potts Model ◽  
Driving Force ◽  
Flow Simulation ◽  
Two Dimensional ◽  
Fluid Regime ◽  
Cellular Potts Model ◽  
Flow Through ◽  
Liquid Foam

Flow through a narrow bent channel may induce topological rearrangements in a two-dimensional monodispersed dry liquid foam. We use the Cellular Potts Model to simulate a foam under a variable driving force in order to investigate the strain-rate response from these rearrangements. We observe a set of foams' behaviors ranging from elastic, viscoelastic to fluid regime. Bubble's topological rearrangements are localized and their cumulative rearrangements change linearly with time, thus nonavalanches critical behavior is found. The strain-rate affects the rate of topological rearrangements, its dependence on the drag force is nonlinear, obeying a Herschel–Bulkley-like relationship below the foam's flow point.

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