Critical Behavior Ising Model S = 1, 3/2 and 2 on Directed Networks

Lima, F. W. S.; Luz, Edina M. S.; Filho, R. N. Costa

doi:10.1163/157361109789017041

Cited by 3 publications

(3 citation statements)

References 18 publications

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“…This leads to the fact that, e.g., on a directed, scale-free Barabási-Albert graph, no spontaneous magnetization can be found and different update algorithms give different results [29]. On directed small-world networks, the S = 1, 3/2 and 2 Ising model, as well as the Blume-Capel model, show a phase transition which changes from second to first order if a specific critical rewiring probability is exceeded [30][31][32]. In the second-order regime, the aforementioned results indicate a different universality class compared to the corresponding models on a regular lattice.…”

Section: Constant Coordination Latticementioning

confidence: 99%

Two-dimensional Ising model on random lattices with constant coordination number

2018

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We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.

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Section: Constant Coordination Latticementioning

confidence: 99%

Two-dimensional Ising model on random lattices with constant coordination number

2018

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“…This means in fact that at all finite temperatures the magnetization eventually vanishes, i.e., no ferromagnetism is present. Lima et al [23] have also studied the Ising model with spin S = 1, 3/2 and 2 on DBA and they have shown that no phase transition is present on these DBA networks.…”

Section: Ising Modelmentioning

confidence: 99%

“…On the other hand, the two-dimensional model has been extended for greater values of spin, namely spin-1, 3/2 and 2 on directed small-world networks (DSW) [23]. In the DSW network [37], Lima et al [23] showed that the two-dimensional Ising model exhibits a second and firstorder phase transition for rewiring probability p = 0.2 and 0.8, respectively, for spin values S = 1, 3/2 and 2. For values p > p c ∼ 0.25 this model presents a first-order phase transition [38].…”

Section: Ising Modelmentioning

confidence: 99%

Magnetic models on various topologies

Lima

Plascak

2014

J. Phys.: Conf. Ser.

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A brief review is given on the study of the thermodynamic properties of spin models defined on different topologies like small-world, scale-free networks, random graphs and regular and random lattices. Ising, Potts and Blume-Capel models are considered. They are defined on complex lattices comprising Appolonian, Barabási-Albert, Voronoi-Delauny and small-world networks. The main emphasis is given on the corresponding phase transitions, transition temperatures, critical exponents and universality, compared to those obtained by the same models on regular Bravais lattices.

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Nonequilibrium model on Apollonian networks

2012

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We investigate the Majority-Vote Model with two states (−1, +1) and a noise q on Apollonian networks. The main result found here is the presence of the phase transition as a function of the noise parameter q. We also studies de effect of redirecting a fraction p of the links of the network. By means of Monte Carlo simulations, we obtained the exponent ratio γ/ν, β/ν, and 1/ν for several values of rewiring probability p. The critical noise was determined qc and U * also was calculated. The effective dimensionality of the system was observed to be independent on p, and the value D ef f ≈ 1.0 is observed for these networks. Previous results on the Ising model in Apollonian Networks have reported no presence of a phase transition. Therefore, the results present here demonstrate that the Majority-Vote Model belongs to a different universality class as the equilibrium Ising Model on Apollonian Network.

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Critical Behavior Ising Model S = 1, 3/2 and 2 on Directed Networks

Cited by 3 publications

References 18 publications

Two-dimensional Ising model on random lattices with constant coordination number

Two-dimensional Ising model on random lattices with constant coordination number

Magnetic models on various topologies

Nonequilibrium model on Apollonian networks

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