Quantum effects on criticality of an Ising model in scale-free networks: Beyond mean-field universality class

2010 ◽  
Vol 81 (1) ◽  
Author(s):  
Hangmo Yi
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
Quantum Effects ◽  
Universality Class ◽  
Scale Free ◽  
Scale Free Networks

A MEAN FIELD APPROACH FOR ISING MODELS ON SCALE-FREE NETWORKS

2011 ◽  
Vol 25 (07) ◽  
pp. 453-464 ◽  
Author(s):  
G. IANNONE ◽  
ORLANDO LUONGO
Keyword(s):  
Ising Model ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Practical Applications ◽  
Scale Free ◽  
Wide Range ◽  
Scale Free Networks ◽  
The Mean ◽  
Mean Field Approximations

Recently, the study of complex networks led to the analysis of the so-called scale-free models in statistical mechanics. This study has increased its importance, thanks to the wide range of applications in numerous physical contexts; for example, one important question is to understand the behavior of various models on such networks. We start first by investigating the Ising model in the mean field approximation and on scale-free networks, studying especially the Ising model with annealed dilution and Clock model, with particular attention devoted to focusing on similarities between the mean field approximations with or without scale-free statistics. A particular emphasis is given to the possible practical applications of these results in other disciplines such as medicine and social science.

FAILURE OF A MEAN-FIELD APPROACH FOR THE MILLER–HUSE PHASE TRANSITION

2000 ◽  
Vol 10 (01) ◽  
pp. 251-256 ◽  
Author(s):  
FRANCISCO SASTRE ◽  
GABRIEL PÉREZ
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Chaotic Maps ◽  
Initial Conditions ◽  
Mean Field ◽  
Region Of Interest ◽  
Universality Class ◽  
Two Dimensional ◽  
Field Approach

The diffusively coupled lattice of odd-symmetric chaotic maps introduced by Miller and Huse undergoes a continuous ordering phase transition, belonging to a universality class close but not identical to that of the two-dimensional Ising model. Here we consider a natural mean-field approach for this model, and find that it does not have a well-defined phase transition. We show how this is due to the coexistence of two attractors in its mean-field description, for the region of interest in the coupling. The behavior of the model in this limit then becomes dependent on initial conditions, as can be seen in direct simulations.

scholarly journals Ising model with invisible states on scale-free networks

2019 ◽  
Vol 383 (27) ◽  
pp. 125844
Author(s):  
Petro Sarkanych ◽  
Mariana Krasnytska
Keyword(s):  
Ising Model ◽  
Scale Free ◽  
Scale Free Networks

Research on SIQRS Spreading Dynamic Model with Feedback Mechanism on Scale-Free Networks

2014 ◽  
Vol 989-994 ◽  
pp. 4524-4527
Author(s):  
Tao Li ◽  
Yuan Mei Wang ◽  
You Ping Yang
Keyword(s):  
Dynamic Model ◽  
Mean Field Theory ◽  
Mean Field ◽  
Feedback Mechanism ◽  
Epidemic Spreading ◽  
Scale Free ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
The Mean ◽  
The Relationship

A modified spreading dynamic model with feedback-mechanism based on scale-free networks is presented in this study. Using the mean field theory, the spreading dynamics of the model is analyzed. The spreading threshold and equilibriums are derived. The relationship between the spreading threshold, the epidemic steady-state and the feedback-mechanism is analyzed in detail. Theoretical results indicate the feedback-mechanism can increase the spreading threshold, resulting in effectively controlling the epidemic spreading.

scholarly journals Six Susceptible-Infected-Susceptible Models on Scale-free Networks

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Satoru Morita
Keyword(s):  
Field Theory ◽  
Mean Field Theory ◽  
Mean Field ◽  
Information Networks ◽  
Propagation Mechanism ◽  
Contact Rate ◽  
Scale Free ◽  
Scale Free Networks ◽  
Information Spread ◽  
Nature And Society

Abstract Spreading phenomena are ubiquitous in nature and society. For example, disease and information spread over underlying social and information networks. It is well known that there is no threshold for spreading models on scale-free networks; this suggests that spread can occur on such networks, regardless of how low the contact rate may be. In this paper, I consider six models with different contact and propagation mechanisms, which include models studied so far, but are apt to be confused. To compare these six models, I analyze them by degree-based mean-field theory. I find that the result depends on the details of contact and propagation mechanism.

Spreading of Epidemics on Scale-Free Networks with Time Delay

2012 ◽  
Vol 562-564 ◽  
pp. 1386-1389
Author(s):  
Yuan Mei Wang ◽  
Tao Li
Keyword(s):  
Field Theory ◽  
Time Delay ◽  
Mean Field Theory ◽  
Mean Field ◽  
Sir Model ◽  
Scale Free ◽  
Spreading Dynamics ◽  
Scale Free Networks ◽  
The Mean ◽  
Theoretical Results

In the SIR model once a node is cured after infection it becomes permanently immune,but we assume this immunity to be temporary. So we obtain an epidemic model with time delay on scale-free networks. Using the mean field theory the spreading threshold and the spreading dynamics is analyzed. Theoretical results indicate that the threshold is significantly dependent on the topology of scale-free networks and time delay. Numerical simulations confirmed the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document