CRITICAL EXPONENTS OF THE CONTINUOUS PHASE TRANSITION IN ZIFF–GULARI–BARSHAD MODEL

A simple irreversible surface reaction model first introduced by Ziff, Gulari and Barshad has been studied using Monte Carlo simulation. We determine the static critical exponents accurately which are in excellent agreement with those of directed percolation universality class.

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Critical exponents and the universality class of a minesweeper percolation model

International Journal of Modern Physics C ◽

10.1142/s0129183120501296 ◽

2020 ◽

Vol 31 (09) ◽

pp. 2050129

Author(s):

Yuqi Qing ◽

Wen-Long You ◽

Maoxin Liu

Keyword(s):

Phase Transition ◽

Monte Carlo Simulation ◽

Monte Carlo ◽

Critical Exponents ◽

Critical Density ◽

Universality Class ◽

Percolation Model ◽

System Configuration ◽

Percolation Transition ◽

Second Order Phase Transition

We introduce a minesweeper percolation model, in which the system configuration is obtained via an automatic minesweeper process. For a variety of candidate networks with different lattice configurations, our process gives rise to a second-order phase transition. Using Monte Carlo simulation, we identify the critical points implied by giant components. A set of critical exponents are extracted to characterize the nature of the minesweeper percolation transition. The determined universality class shows a clear difference from the traditional percolation transition. A proper mine density of the minesweeper game should be set around the critical density.

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Critical exponents for an irreversible surface reaction model

Physical Review A ◽

10.1103/physreva.41.3411 ◽

1990 ◽

Vol 41 (6) ◽

pp. 3411-3414 ◽

Cited By ~ 159

Author(s):

Iwan Jensen ◽

Hans C. Fogedby ◽

Ronald Dickman

Keyword(s):

Critical Exponents ◽

Surface Reaction ◽

Reaction Model ◽

Surface Reaction Model

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CO+NO surface reaction model by Monte Carlo simulation

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2003.01.002 ◽

2004 ◽

Vol 331 (3-4) ◽

pp. 505-516 ◽

Cited By ~ 3

Author(s):

J.J. Luque ◽

A. Gómez ◽

A. Córdoba

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Surface Reaction ◽

Reaction Model ◽

Surface Reaction Model

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Monte Carlo simulation of a surface reaction model with local interaction

The Journal of Chemical Physics ◽

10.1063/1.462306 ◽

1992 ◽

Vol 96 (11) ◽

pp. 8535-8538 ◽

Cited By ~ 29

Author(s):

J. J. Luque ◽

F. Jiménez‐Morales ◽

M. C. Lemos

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Surface Reaction ◽

Reaction Model ◽

Local Interaction ◽

Surface Reaction Model

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Kinetic phase transition of the dimer-dimer surface reaction model

Physical Review E ◽

10.1103/physreve.58.234 ◽

1998 ◽

Vol 58 (1) ◽

pp. 234-240 ◽

Cited By ~ 8

Author(s):

Hou Zhonghuai ◽

Yang Lingfa ◽

Xin Houwen

Keyword(s):

Phase Transition ◽

Surface Reaction ◽

Reaction Model ◽

Kinetic Phase Transition ◽

Surface Reaction Model

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Criticality between cortical states

10.1101/454934 ◽

2018 ◽

Author(s):

Antonio J. Fontenele ◽

Nivaldo A. P. de Vasconcelos ◽

Thaís Feliciano ◽

Leandro A. A. Aguiar ◽

Carina Soares-Cunha ◽

...

Keyword(s):

Phase Transition ◽

Cerebral Cortex ◽

Critical Exponents ◽

Slow Wave Sleep ◽

Mean Field ◽

Universality Class ◽

Directed Percolation ◽

Intermediate Value ◽

Neuronal Avalanches ◽

The Brain

Since the first measurements of neuronal avalanches [1], the critical brain hypothesis has gained traction [2]. However, if the brain is critical, what is the phase transition? For several decades it has been known that the cerebral cortex operates in a diversity of regimes [3], ranging from highly synchronous states (e.g. slow wave sleep [4], with higher spiking variability) to desynchronized states (e.g. alert waking [5], with lower spiking variability). Here, using independent signatures of criticality, we show that a phase transition occurs in an intermediate value of spiking variability. The critical exponents point to a universality class different from mean-field directed percolation (MF-DP). Importantly, as the cortex hovers around this critical point [6], it follows a linear relation between the avalanche exponents that encompasses previous experimental results from different setups [7, 8] and is reproduced by a model.

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Kinetic Models of Discrete Opinion Dynamics on Directed Barabási–Albert Networks

Entropy ◽

10.3390/e21100942 ◽

2019 ◽

Vol 21 (10) ◽

pp. 942 ◽

Cited By ~ 3

Author(s):

F. Welington S. Lima ◽

J. A. Plascak

Keyword(s):

Phase Transition ◽

Monte Carlo ◽

Kinetic Models ◽

Order Parameter ◽

Majority Vote ◽

Opinion Dynamics ◽

Universality Class ◽

Continuous Phase ◽

Vote Model ◽

Continuous Phase Transition

Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity of these directed networks. In addition, the ratio of the critical exponents of the order parameter and the corresponding susceptibility to the correlation length have also been computed. It is noticed that the kinetic model and the majority-vote model on these directed Barabási–Albert networks are in the same universality class.

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