scholarly journals MONTE CARLO SIMULATIONS OF A DISORDERED BINARY ISING MODEL

2012 ◽  
Vol 23 (08) ◽  
pp. 1240015 ◽  
Author(s):  
D. S. CAMBUÍ ◽  
A. S. DE ARRUDA ◽  
M. GODOY
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Critical Exponents ◽  
Nearest Neighbor ◽  
Spin Exchange ◽  
Exchange Interactions ◽  
Square Lattice ◽  
Critical Temperatures

A disordered binary Ising model, with only nearest-neighbor spin exchange interactions J > 0 on the square lattice, is studied through Monte Carlo simulations. The system consists of two different particles with spin-1/2 and spin-1, randomly distributed on the lattice. We found the critical temperatures for several values of the concentration x of spin-1/2 particles, and also the corresponding critical exponents.

Kinetics of B2, DO3, and B32 ordering: Results from pair approximation calculations and Monte Carlo simulations

1994 ◽  
Vol 9 (2) ◽  
pp. 348-356 ◽  
Author(s):  
L. Anthony ◽  
B. Fultz
Keyword(s):  
Monte Carlo ◽  
Kinetic Theory ◽  
Monte Carlo Simulations ◽  
Nearest Neighbor ◽  
Pair Approximation ◽  
Probability Method ◽  
Critical Temperatures ◽  
Point Pair ◽  
Bcc Lattice ◽  
Kinetics Of

A kinetic theory of ordering based on the path probability method was implemented in the pair (Bethe) approximation and used to study the kinetics of short- and long-range ordering in alloys with equilibrium states of B2, DO3, or B32 order. The theory was developed in a superposition approximation for a vacancy mechanism on a bcc lattice with first- (1nn) and second-nearest neighbor (2nn) pair interactions. Chained 1nn conditional probabilities were used to account for the entropy of 2nn pair configurations. Monte Carlo simulations of ordering were also performed and their results compared to predictions of the pair approximation. Comparisons are also made with predictions from an earlier kinetic theory implemented in the point (Bragg-Williams) approximation. For all three calculations (point, pair, and Monte Carlo), critical temperatures for B2 and DO3 ordering are reported for different 1nn and 2nn interaction strengths. The influence of annealing temperature on the kinetic paths through the space of B2, DO3, and B32 order parameters was found to be strong when the thermodynamic preferences for the ordered states were of similar strengths. Transient states of intermediate order were also studied. A transient formation of B32 order in an AB3 alloy was found when 2nn interactions were strong, even when B32 order was neither a Richards-Allen-Cahn ground state nor a stable equilibrium state at that temperature. The formation of this transient B32 order can be argued consistently from a thermodynamic perspective. However, a second example of transient B2 order in an AB alloy with equilibrium B32 order cannot be explained by the same thermodynamic argument, and we believe that its origin is primarily kinetic.

LONG-RANGE ORDER FOR THE 3-STATE SQUARE LATTICE POTTS MODEL WITH ANTIFERROMAGNETIC “THE MOVE OF THE KNIGHT” INTERACTIONS

1996 ◽  
Vol 10 (15) ◽  
pp. 731-736
Author(s):  
A.V. BAKAEV ◽  
V.I. KABANOVICH
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Long Range ◽  
Potts Model ◽  
Ground State ◽  
Nearest Neighbor ◽  
Two Dimensions ◽  
Range Order ◽  
Square Lattice ◽  
Long Range Order

The 3-state square lattice Potts model with interactions of spins belonging to the different sublattices, the nearest-neighbor (NN) interaction and “the move of the knight” (MK) antiferromagnetic interactions which also couples spins on the sublattice A to spins on B, is studied by Monte Carlo simulations. It is shown that the MK-interactions stabilizes the BSS phase in two dimensions, preserving macroscopic degeneracy of the ground state. In a range of competing ferromagnetic (NN) interactions “stripes” or “double-stripes” phases are found.

scholarly journals MAJORITY-VOTE MODEL ON (3, 4, 6, 4) AND (34, 6) ARCHIMEDEAN LATTICES

2006 ◽  
Vol 17 (09) ◽  
pp. 1273-1283 ◽  
Author(s):  
F. W. S. LIMA ◽  
K. MALARZ
Keyword(s):  
Phase Transition ◽  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Critical Exponents ◽  
Majority Vote ◽  
Embedding Dimension ◽  
Vote Model ◽  
Disorder Phase Transition ◽  
Regular Lattices

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Two examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are qc = 0.091(2) and qc = 0.134(3) for (3, 4, 6, 4) and (34, 6) Archimedean lattices, respectively. The critical exponents β/ν, γ/ν and 1/ν for this model are 0.103 (6), 1.596 (54), 0.872 (85) for (3, 4, 6, 4) and 0.114 (3), 1.632 (35), 0.98 (10) for (34, 6) Archimedean lattices. These results differs from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks. The effective dimensionalities of the system [D eff (3, 4, 6, 4) = 1.802(55) and D eff (34, 6) = 1.860(34)] for these networks are reasonably close to the embedding dimension two.

scholarly journals Critical Behaviour of the Ising S=l/2 and S=l Model on (3,4,6,4) and (3,3,3,3,6) Archimedean Lattices

2011 ◽  
Vol 10 (4) ◽  
pp. 912-919 ◽  
Author(s):  
F. W. S. Lima ◽  
J. Mostowicz ◽  
K. Malarz
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Monte Carlo Simulations ◽  
Critical Exponents ◽  
Finite Size ◽  
Square Lattice ◽  
Scaling Analysis ◽  
Critical Properties ◽  
Finite Size Scaling ◽  
Effective Dimensionality

AbstractWe investigate the critical properties of the Ising S = 1/2 and S = 1 model on (3,4,6,4) and (34,6) Archimedean lattices. The system is studied through the extensive Monte Carlo simulations. We calculate the critical temperature as well as the critical point exponents γ/ν, β/ν, and ν basing on finite size scaling analysis. The calculated values of the critical temperature for S = 1 are kBTC/J=1.590(3), and kBTC/J=2.100(4) for (3,4,6,4) and (34,6) Archimedean lattices, respectively. The critical exponents β/ν, γ/ν, and 1/ν, for S=1 are β/ν=0.180(20), γ/ν=1.46(8), and 1/ν=0.83(5), for (3,4,6,4) and 0.103(8), 1.44(8), and 0.94(5), for (34,6) Archimedean lattices. Obtained results differ from the Ising S = 1/2 model on (3,4,6,4), (34,6) and square lattice. The evaluated effective dimensionality of the system for S = 1 are Deff=1.82(4), for (3,4,6,4), and Deff = 1.64(5) for (34,6).

Monte Carlo simulations of long-range order kinetics in B2 phases

1995 ◽  
Vol 10 (3) ◽  
pp. 591-595 ◽  
Author(s):  
K. Yaldram ◽  
V. Pierron-Bohnes ◽  
M.C. Cadeville ◽  
M.A. Khan
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Nearest Neighbor ◽  
Vacancy Concentration ◽  
Relaxation Times ◽  
Nearest Neighbors ◽  
Migration Energy ◽  
Ordering Kinetics ◽  
Migration Barriers ◽  
Temperature Dependences

The thermodynamic parameters that drive the atomic migration in B2 alloys are studied using Monte-Carlo simulations. The model is based on a vacancy jump mechanism between nearest neighbor sites, with a constant vacancy concentration. The ordering energy is described through an Ising Hamiltonian with interaction potentials between first and second nearest neighbors. Different migration barriers are introduced fur A and B atoms. The results of the simulations compare very well with those of experiments. The ordering kinetics are well described by exponential-like behaviors with two relaxation times whose temperature dependences are Arrhenius laws yielding effective migration energies. The ordering energy contributes significantly to the total migration energy.

Non-Equilibrium Critical Relaxation of Heisenberg Ferromagnets with Long-Range Correlated Defects

2012 ◽  
Vol 190 ◽  
pp. 39-42
Author(s):  
M. Medvedeva ◽  
Pavel V. Prudnikov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Heisenberg Model ◽  
Three Dimensional ◽  
Initial State ◽  
Short Time ◽  
Theoretic Description ◽  
Good Agreement

The dynamic critical behavior of the three-dimensional Heisenberg model with longrangecorrelated disorder was studied by using short-time Monte Carlo simulations at criticality.The static and dynamic critical exponents are determined. The simulation was performed fromordered initial state. The obtained values of the exponents are in a good agreement with resultsof the field-theoretic description of the critical behavior of this model in the two-loopapproximation.

Exact site-percolation probability on the square lattice

2021 ◽  
Author(s):  
Stephan Mertens
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Percolation Threshold ◽  
Percolation Cluster ◽  
Square Lattice ◽  
Site Percolation ◽  
Exact Probability ◽  
Percolation Probability ◽  
A Site ◽  
Time And Space Complexity

Abstract We present an algorithm to compute the exact probability $R_{n}(p)$ for a site percolation cluster to span an $n\times n$ square lattice at occupancy $p$. The algorithm has time and space complexity $O(\lambda^n)$ with $\lambda \approx 2.6$. It allows us to compute $R_{n}(p)$ up to $n=24$. We use the data to compute estimates for the percolation threshold $p_c$ that are several orders of magnitude more precise than estimates based on Monte-Carlo simulations.

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