scholarly journals Mean-field analysis of the majority-vote model broken-ergodicity steady state

2012 ◽  
Vol 2012 (07) ◽  
pp. P07003 ◽  
Author(s):  
Paulo F C Tilles ◽  
José F Fontanari
Keyword(s):  
Steady State ◽  
Majority Vote ◽  
Mean Field ◽  
Field Analysis ◽  
Vote Model

scholarly journals Ferromagnetic and spin-glass-like transition in the majority vote model on complete and random graphs

2020 ◽  
Vol 93 (9) ◽  
Author(s):  
Andrzej Krawiecki
Keyword(s):  
Spin Glass ◽  
Random Graphs ◽  
Thermal Noise ◽  
Theoretical Calculations ◽  
Majority Vote ◽  
Mean Field ◽  
Ferromagnetic Phase ◽  
Thermal Bath ◽  
Opinion Formation ◽  
Vote Model

Abstract Ferromagnetic and spin-glass-like transitions in nonequilibrium spin models in contact with two thermal baths with different temperatures are investigated. The models comprise the Sherrington-Kirkpatrick model and the dilute spin glass model which are the Ising models on complete and random graphs, respectively, with edges corresponding, with certain probability, to positive and negative exchange integrals. The spin flip rates are combinations of two Glauber rates at the two temperatures, and by varying the coefficients of this combination probabilities of contact of the model with each thermal bath and thus the level of thermal noise in the model are changed. Particular attention is devoted to the majority vote model in which one of the two above-mentioned temperatures is zero and the other one tends to infinity. Only in rare cases such nonequilibrium models can be mapped onto equilibrium ones at certain effective temperature. Nevertheless, Monte Carlo simulations show that transitions from the paramagnetic to the ferromagnetic and spin-glass-like phases occur in all cases under study as the level of thermal noise is varied, and the phase diagrams resemble qualitatively those for the corresponding equilibrium models obtained with varying temperature. Theoretical investigation of the model on complete and random graphs is performed using the TAP equations as well as mean-field and pair approximations, respectively. In all cases theoretical calculations yield reasonably correct predictions concerning location of the phase border between the paramagnetic and ferromagnetic phases. In the case of the spin-glass-like transition only qualitative agreement between theoretical and numerical results is achieved using the TAP equations, and the mean-field and pair approximations are not suitable for the study of this transition. The obtained results can be interesting for modeling opinion formation by means of the majority-vote and related models and suggest that in the presence of negative interactions between agents, apart from the ferromagnetic phase corresponding to consensus formation, spin-glass-like phase can occur in the society characterized by local rather than long-range ordering. Graphical abstract

scholarly journals Quenched mean-field theory for the majority-vote model on complex networks

2017 ◽  
Vol 120 (1) ◽  
pp. 18003 ◽  
Author(s):  
Feng Huang ◽  
Hanshuang Chen ◽  
Chuansheng Shen
Keyword(s):  
Field Theory ◽  
Complex Networks ◽  
Majority Vote ◽  
Mean Field Theory ◽  
Mean Field ◽  
Vote Model

scholarly journals Majority-vote model on spatially embedded networks: Crossover from mean-field to Ising universality classes

2016 ◽  
Vol 93 (5) ◽  
Author(s):  
C. I. N. Sampaio Filho ◽  
T. B. dos Santos ◽  
A. A. Moreira ◽  
F. G. B. Moreira ◽  
J. S. Andrade
Keyword(s):  
Majority Vote ◽  
Mean Field ◽  
Vote Model ◽  
Embedded Networks ◽  
Universality Classes

scholarly journals Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Bartłomiej Nowak ◽  
Katarzyna Sznajd-Weron
Keyword(s):  
Phase Transitions ◽  
Complete Graph ◽  
Order Parameter ◽  
Threshold Model ◽  
Majority Vote ◽  
Mean Field ◽  
Exact Result ◽  
Continuous Phase ◽  
Vote Model ◽  
Discontinuous Phase

We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so-called independence, whereas in the second version anticonformity plays the role of a noise, which destroys the order. The modified Watts threshold model, studied here, is homogeneous and possesses an up-down symmetry, which makes it similar to other binary opinion models with a single-flip dynamics, such as the majority-vote and the q-voter models. Because within the majority-vote model with independence only continuous phase transitions are observed, whereas within the q-voter model with independence also discontinuous phase transitions are possible, we ask the question about the factor, which could be responsible for discontinuity of the order parameter. We investigate the model via the mean-field approach, which gives the exact result in the case of a complete graph, as well as via Monte Carlo simulations. Additionally, we provide a heuristic reasoning, which explains observed phenomena. We show that indeed if the threshold r=0.5, which corresponds to the majority-vote model, an order-disorder transition is continuous. Moreover, results obtained for both versions of the model (one with independence and the second one with anticonformity) give the same results, only rescaled by the factor of 2. However, for r>0.5 the jump of the order parameter and the hysteresis is observed for the model with independence, and both versions of the model give qualitatively different results.

scholarly journals Modules or Mean-Fields?

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 552 ◽  
Author(s):  
Thomas Parr ◽  
Noor Sajid ◽  
Karl J. Friston
Keyword(s):  
Steady State ◽  
Message Passing ◽  
Mean Field Theory ◽  
Functional Anatomy ◽  
Mean Field ◽  
State Density ◽  
Stochastic Dynamical Systems ◽  
Conditional Independency ◽  
The Brain ◽  
Non Equilibrium

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

scholarly journals Mean Field Analysis of Orientation Selective Grain Growth Driven By Interface-Energy Anisotropy

1994 ◽  
Vol 343 ◽  
Author(s):  
J. A. Floro ◽  
C. V. Thompson
Keyword(s):  
Grain Size ◽  
Size Distribution ◽  
Grain Growth ◽  
Texture Evolution ◽  
Mean Field ◽  
Orientation Distribution ◽  
Interface Energy ◽  
Abnormal Grain Growth ◽  
Field Analysis ◽  
Energy Anisotropy

ABSTRACTAbnormal grain growth is characterized by the lack of a steady state grain size distribution. In extreme cases the size distribution becomes transiently bimodal, with a few grains growing much larger than the average size. This is known as secondary grain growth. In polycrystalline thin films, the surface energy γs and film/substrate interfacial energy γi vary with grain orientation, providing an orientation-selective driving force that can lead to abnormal grain growth. We employ a mean field analysis that incorporates the effect of interface energy anisotropy to predict the evolution of the grain size/orientation distribution. While abnormal grain growth and texture evolution always result when interface energy anisotropy is present, whether secondary grain growth occurs will depend sensitively on the details of the orientation dependence of γi.

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