Application of the Monte Carlo Method to the Lattice‐Gas Model. I. Two‐Dimensional Triangular Lattice

1959 ◽  
Vol 30 (1) ◽  
pp. 65-72 ◽  
Author(s):  
Z. W. Salsburg ◽  
J. D. Jacobson ◽  
W. Fickett ◽  
W. W. Wood
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Triangular Lattice ◽  
Lattice Gas ◽  
Lattice Gas Model ◽  
Two Dimensional ◽  
The Monte Carlo Method

Two-dimensional Janus-like particles on a triangular lattice

Soft Matter ◽  
2020 ◽  
Vol 16 (28) ◽  
pp. 6633-6642
Author(s):  
A. Patrykiejew ◽  
W. Rżysko
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Triangular Lattice ◽  
Canonical Ensemble ◽  
Grand Canonical Ensemble ◽  
Dimensional System ◽  
Two Dimensional ◽  
The Monte Carlo Method ◽  
Two Dimensional System ◽  
Grand Canonical

We have studied the phase behavior of a two-dimensional system of Janus-like particles on a triangular lattice using the Monte Carlo method in a grand canonical ensemble.

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.

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.

Numerical solution of the multidimensional Gelfand–Levitan equation

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Sergey I. Kabanikhin ◽  
Karl K. Sabelfeld ◽  
Nikita S. Novikov ◽  
Maxim A. Shishlenin
Keyword(s):  
Inverse Problem ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Two Dimensional ◽  
Nonlinear Inverse Problem ◽  
Coefficient Inverse Problem ◽  
Specific Point ◽  
The Monte Carlo Method ◽  
Linear Integral ◽  
Linear Integral Equations

AbstractThe coefficient inverse problem for the two-dimensional wave equation is solved. We apply the Gelfand–Levitan approach to transform the nonlinear inverse problem to a family of linear integral equations. We consider the Monte Carlo method for solving the Gelfand–Levitan equation. We obtain the estimation of the solution of the Gelfand–Levitan equation in one specific point, due to the properties of the method. That allows the Monte Carlo method to be more effective in terms of span cost, compared with regular methods of solving linear system. Results of numerical simulations are presented.

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.

The evolution of pairing correlation in the anisotropic triangular lattice

2017 ◽  
Vol 28 (10) ◽  
pp. 1750127
Author(s):  
Jingyao Wang ◽  
Yamei Zeng ◽  
Peng Wang ◽  
Ying Liang ◽  
Tianxing Ma
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Triangular Lattice ◽  
Quantum Monte Carlo ◽  
Two Dimensional ◽  
Pairing Correlation ◽  
Pairing Symmetries ◽  
Charge Transfer Salts ◽  
Quantum Monte Carlo Method ◽  
Superconducting Pairing

By using the determined quantum Monte Carlo method, we explore the evolution of the pairing correlation depending on doping and frustration in the two-dimensional Hubbard model on an anisotropic triangular lattice. In the full frustrated system where the nearest hoping term [Formula: see text] is equal to the next nearest hoping [Formula: see text], the [Formula: see text]-wave pairing dominates over [Formula: see text] as the electron filling [Formula: see text]. The [Formula: see text] superconducting pairing tends to be dominated as the frustration [Formula: see text] decreases, and the decreasing electron fillings also push the system into a possible [Formula: see text] superconducting state. Our intensive nonbiased numerical results reveal the competition between [Formula: see text] and [Formula: see text] superconducting pairing states, clarifying the different pairing symmetries in the [Formula: see text]-(BEDT-TTF)[Formula: see text] family of organic charge transfer salts.

Equilibrium and nonequilibrium models on Solomon networks

2016 ◽  
Vol 27 (11) ◽  
pp. 1650134 ◽  
Author(s):  
F. W. S. Lima
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Critical Exponents ◽  
Majority Vote ◽  
Universality Class ◽  
Nonequilibrium Systems ◽  
Two Dimensional ◽  
Critical Properties ◽  
The Monte Carlo Method ◽  
Regular Lattices

We investigate the critical properties of the equilibrium and nonequilibrium systems on Solomon networks. The equilibrium and nonequilibrium systems studied here are the Ising and Majority-vote models, respectively. These systems are simulated by applying the Monte Carlo method. We calculate the critical points, as well as the critical exponents ratio [Formula: see text], [Formula: see text] and [Formula: see text]. We find that both systems present identical exponents on Solomon networks and are of different universality class as the regular two-dimensional ferromagnetic model. Our results are in agreement with the Grinstein criterion for models with up and down symmetry on regular lattices.

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