Susceptibility of the Ising model on the scale-free network with a Cayley tree-like structure

2008 ◽  
Vol 387 (5-6) ◽  
pp. 1404-1410 ◽  
Author(s):  
Takehisa Hasegawa ◽  
Koji Nemoto
Keyword(s):  
Ising Model ◽  
Cayley Tree ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

PHASE TRANSITION IN THE ISING MODEL ON LOCAL-WORLD EVOLVING NETWORKS

2008 ◽  
Vol 19 (11) ◽  
pp. 1717-1726
Author(s):  
WEI QIANG ◽  
GUANGDAO HU ◽  
PENGDA ZHAO
Keyword(s):  
Phase Transition ◽  
Critical Temperature ◽  
Ising Model ◽  
Scale Free Network ◽  
Scale Free ◽  
Evolving Networks ◽  
Free Network ◽  
Effective Phase ◽  
Limiting Case ◽  
Ising Spins

We study the critical behavior of the Ising model on the local-world evolving network. Monte Carlo simulations with the standard Metropolis local update algorithms are performed extensively on the network with different parameters. Ising spins put onto network vertices exhibit an effective phase transition from ferromagnetism to paramagnetism upon heating. The critical temperature has been demonstrated to increase linearly with the average degree of the network as TC ~ 〈k〉. Simulation results on local-world evolving networks with various parameters show logarithmical relationships of the critical temperature with the size of the local world as TC ~ ln (ml), and with the size of the network as TC ~ ln (N), respectively. The latter is the generalization of the conclusion for the Ising model on the Barabási–Albert scale-free network, a limiting case of the local-world evolving network.

scholarly journals On the discontinuity of the specific heat of the Ising model on a scale-free network

2015 ◽  
Vol 18 (4) ◽  
pp. 44601
Author(s):  
Krasnytska ◽  
Berche ◽  
Holovatch ◽  
Kenna
Keyword(s):  
Ising Model ◽  
Specific Heat ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network

scholarly journals Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1175
Author(s):  
Mariana Krasnytska ◽  
Bertrand Berche ◽  
Yurij Holovatch ◽  
Ralph Kenna
Keyword(s):  
Exact Solution ◽  
Ising Model ◽  
Thermodynamic Functions ◽  
Power Laws ◽  
Scale Free Network ◽  
Variable Properties ◽  
Scale Free ◽  
Logarithmic Corrections ◽  
Free Network ◽  
Universality Classes

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes.

SELF-ORGANIZED NETWORKS AS A REPRESENTATION OF QUANTUM STATISTICS

2000 ◽  
Vol 14 (29n31) ◽  
pp. 3356-3361 ◽  
Author(s):  
GINESTRA BIANCONI
Keyword(s):  
Cayley Tree ◽  
Scale Free Network ◽  
Quantum Distribution ◽  
Scale Free ◽  
New Class ◽  
Self Organized ◽  
Different Types ◽  
Free Network ◽  
The Right ◽  
Quantum Distributions

A new class of self organized networks is described that is relevant to understand the emerging order in a large number of complex systems such as growing biological systems, the web, and heterogeneous phases of correlated condensed matter systems formed by doping. The Bose and Fermi quantum distributions are shown to be the right tool to describe the two extreme limit distributions, the fermionic Cayley-tree network and the bosonic scale-free network. In this new large class of self-organized networks the two different types of self organization coexists, maintaining the same 'ergodic' nature and are described by a 'mixed' quantum distribution.

Research on new evolution model of scale-free network

2009 ◽  
Vol 29 (5) ◽  
pp. 1230-1232
Author(s):  
Hao RAO ◽  
Chun YANG ◽  
Shao-hua TAO
Keyword(s):  
Evolution Model ◽  
Scale Free Network ◽  
Scale Free ◽  
Free Network
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