Stochastic bifurcations in the nonlinear parallel Ising model

Bagnoli, Franco; Rechtman, Raúl

doi:10.1103/physreve.94.052111

Cited by 3 publications

(3 citation statements)

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“…For p 1 p p 2 , we find two attractors, one (in red, lighter) in the lower branches, and the other one (in blue, darker) in the top ones. A similar bifurcation diagram can be seen also in the parallel Ising model with plaquette terms (see [53]).…”

Section: Network Influence and Small World Transitionssupporting

confidence: 66%

“…In the language of magnetic systems, this effect can be translated into a "plaquette" term, i.e., a term that depends on the presence of a certain number of aligned spins in the neighborhood. It can be easily verified that this influence can be translated in terms involving the products of more than two spins or, equivalently, in powers of the local magnetic field [53]. Thus, one can consider for instance Hamiltonians of the form…”

Section: The Time Average Of An Observable Ismentioning

confidence: 99%

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Percolation and Internet Science

et al. 2019

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Percolation, in its most general interpretation, refers to the “flow” of something (a physical agent, data or information) in a network, possibly accompanied by some nonlinear dynamical processes on the network nodes (sometimes denoted reaction–diffusion systems, voter or opinion formation models, etc.). Originated in the domain of theoretical and matter physics, it has many applications in epidemiology, sociology and, of course, computer and Internet sciences. In this review, we illustrate some aspects of percolation theory and its generalization, cellular automata and briefly discuss their relationship with equilibrium systems (Ising and Potts models). We present a model of opinion spreading, the role of the topology of the network to induce coherent oscillations and the influence (and advantages) of risk perception for stopping epidemics. The models and computational tools that are briefly presented here have an application to the filtering of tainted information in automatic trading. Finally, we introduce the open problem of controlling percolation and other processes on distributed systems.

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Section: Network Influence and Small World Transitionssupporting

confidence: 66%

Section: The Time Average Of An Observable Ismentioning

confidence: 99%

Percolation and Internet Science

et al. 2019

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“…Approaches closely related to ours have been employed in [23,24]; their interacting particle systems, however, evolve in continuous time and are not homogeneous in space. A somewhat related approach has also appeared in the sociophysics literature [25]. This paper is structured as follows.…”

Section: Introductionmentioning

confidence: 99%

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects

Mendonça

Gevorgyan

2017

Phys. Rev. E

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We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with nonoverlapping generations. Beginning with a general six-parameter model, we find constraints on the transition probabilities of the PCA that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof. Several possible models display a negative cubic term that can be interpreted as a weak Allee factor. We also investigate the conditions under which a one-parameter PCA derived from the more general six-parameter model can generate valid population growth dynamics. Numerical simulations illustrate the behavior of some of the PCA found.

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How can we reach consensus? The answer from the micro-configurations of a 2-D Ising model

Wang

Hou

et al. 2020

Int. J. Mod. Phys. C

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We study opinion formation by uncovering the relevant aspects hiding in the distribution of micro-configurations in a 2-D Ising model. The external field denotes the external influence such as guiding viewpoint, and temperature represents randomness of the agents. The full-positive configuration or the full-negative configuration means consensus. We find that the probability of the full-positive configuration and the full-negative configuration can reach [Formula: see text] (which implies the equal splitting of a group) if the interaction is strong enough and the system is free from external field; the probability of the full-positive configuration can reach 1 (which means consensus) if the positive external field is strong enough under condition of given interaction and temperature. These phenomena are regarded as the reversing mechanism of the full-negative configuration induced by the external field — an opinion reversal. The equal splitting and consensus can be broken down as temperature rises. We discuss the dependence of interaction strength [Formula: see text] (with which the equal splitting occurs) on temperature [Formula: see text], the dependence of external field strength [Formula: see text] (with which the consensus occurs) on interaction strength [Formula: see text] at a certain temperature, as well as the scaling relations responsible for the probability of the full-negative configuration varying with temperature under different conditions. The findings provide us with a good description to understand opinion formation.

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Stochastic bifurcations in the nonlinear parallel Ising model

Cited by 3 publications

References 50 publications

Percolation and Internet Science

Percolation and Internet Science

Approximate probabilistic cellular automata for the dynamics of single-species populations under discrete logisticlike growth with and without weak Allee effects

How can we reach consensus? The answer from the micro-configurations of a 2-D Ising model

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