Equilibrium and nonequilibrium models on solomon networks with two square lattices

We investigate the critical properties of the equilibrium and nonequilibrium two-dimensional (2D) systems on Solomon networks with both nearest and random neighbors. The equilibrium and nonequilibrium 2D systems studied here by Monte Carlo simulations are the Ising and Majority-vote 2D models, respectively. We calculate the critical points as well as the critical exponent ratios [Formula: see text], [Formula: see text], and [Formula: see text]. We find that numerically both systems present the same exponents on Solomon networks (2D) and are of different universality class than the regular 2D 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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Equilibrium and nonequilibrium models on Solomon networks

International Journal of Modern Physics C ◽

10.1142/s0129183116501345 ◽

2016 ◽

Vol 27 (11) ◽

pp. 1650134 ◽

Cited By ~ 1

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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FISHER SCALING IN TWO-DIMENSIONAL ISING MAGNETIC LATTICE-GAS

International Journal of Modern Physics C ◽

10.1142/s0129183105006929 ◽

2005 ◽

Vol 16 (01) ◽

pp. 45-60 ◽

Cited By ~ 3

Author(s):

A. L. FERREIRA ◽

E. L. PRODANESCU

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Specific Heat ◽

Lattice Gas ◽

Canonical Ensemble ◽

Universality Class ◽

Lattice Gas Model ◽

Two Dimensional ◽

Critical Properties

The critical properties of two-dimensional Ising magnetic lattice-gas model are studied by Monte-Carlo simulation in the canonical ensemble. The results are analyzed considering the modified Fisher scaling for systems with zero specific heat exponent, which applies when there are constrained variables such as the density in the canonical ensemble. The estimates of the exponents are obtained and compared to the exponents of the Ising universality class to which the model is expected to belong.

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Dynamic critical exponent z of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model

Physical Review E ◽

10.1103/physreve.101.022126 ◽

2020 ◽

Vol 101 (2) ◽

Author(s):

Martin Hasenbusch

Keyword(s):

Monte Carlo ◽

Monte Carlo Simulations ◽

Critical Exponent ◽

Three Dimensional ◽

Universality Class

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

International Journal of Modern Physics C ◽

10.1142/s0129183106009849 ◽

2006 ◽

Vol 17 (09) ◽

pp. 1273-1283 ◽

Cited By ~ 37

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.

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