Metastable States in the Parallel Ising Model

Bagnoli, Franco; Matteuzzi, Tommaso; Rechtman, Raúl

doi:10.5506/aphyspolbsupp.9.25

Cited by 2 publications

(3 citation statements)

References 21 publications

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“…The parallel version of the linear (W = 0) Ising model does not show many differences with respect to the standard serial one [38]. The observables that depend only on single-site properties take the same values in parallel or sequential dynamics [39], although differences arise for two-site correlations [52]. In general the resulting dynamics is no more reversible with respect to the Gibbs measure induced by any Hamiltonian [40].…”

Section: Parallel Nonlinear Ising Modelmentioning

confidence: 99%

Stochastic bifurcations in the nonlinear parallel Ising model

Bagnoli

Rechtman

2016

Phys. Rev. E

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We investigate the phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations, by changing the couplings or the connectivity. The spatial model shows bifurcations in the average magnetization, similar to what seen in the mean-field approximation, induced by the change of the topology, after rewiring short-range to long-range connection, as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution (degree of asynchronism) of the updating. We also examined the effects of inhomogeneity, mixing ferromagnetic and antiferromagnetic coupling, which induces an unexpected bifurcation diagram with a "bubbling" behavior, as also happens for dilution.

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Section: Parallel Nonlinear Ising Modelmentioning

confidence: 99%

Stochastic bifurcations in the nonlinear parallel Ising model

Bagnoli

Rechtman

2016

Phys. Rev. E

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“…We introduce the dilution d in a way similar to what has been done in the sister article [9]. The dilution d is the fraction of sites chosen at random that are not updated at every time step, i.e., a measure of the asynchronism of the updating rule.…”

Section: Partial Asynchronism (Dilution)mentioning

confidence: 99%

“…The dynamical model can be updated in a sequential or parallel order; the sequential dynamics brings to the equilibrium distribution (in the case of symmetric couplings), while the fully parallel version has a different equilibrium distribution [10], although many observables like the magnetization take the same value [9,11].…”

Section: It Is Clear Thatmentioning

confidence: 99%

Topological Phase Transitions in the Nonlinear Parallel Ising Model

Bagnoli¹,

Matteuzzi²,

Rechtman³

2016

Acta Phys. Pol. B Proc. Suppl.

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We investigate some phase transitions of a nonlinear, parallel version of the Ising model, characterized by an antiferromagnetic linear coupling and a ferromagnetic nonlinear one. This model arises in problems of opinion formation. The mean-field approximation shows chaotic oscillations by changing the linear coupling or the connectivity. The spatial model exhibits bifurcations in the average magnetization, similar to what is seen in the mean-field approximation induced by the change of the topology, after rewiring short-range to long-range connections as predicted by the small-world effect. These coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins, induced by long-range couplings. Similar bifurcations may be induced in the randomly connected model by changing the coupling or the connectivity and the synchronism of the updating (dilution of the rule).

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Metastable States in the Parallel Ising Model

Cited by 2 publications

References 21 publications

Stochastic bifurcations in the nonlinear parallel Ising model

Stochastic bifurcations in the nonlinear parallel Ising model

Topological Phase Transitions in the Nonlinear Parallel Ising Model

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