scholarly journals Zero temperature dynamics of Ising model on a densely connected small world network

2005 ◽  
Vol 47 (3) ◽  
pp. 391-396 ◽  
Author(s):  
Pratap Kumar Das ◽  
Parongama Sen
Keyword(s):  
Ising Model ◽  
Small World ◽  
Small World Network ◽  
Zero Temperature ◽  
Temperature Dynamics

scholarly journals Comment on “Ising model on a small world network”

2002 ◽  
Vol 66 (1) ◽  
Author(s):  
H. Hong ◽  
Beom Jun Kim ◽  
M. Y. Choi
Keyword(s):  
Ising Model ◽  
Small World ◽  
Small World Network

ISING MODEL ON A SMALL WORLD NETWORK

2004 ◽  
Vol 18 (17n19) ◽  
pp. 2575-2578 ◽  
Author(s):  
TIAN-YI CAI ◽  
ZHEN-YA LI
Keyword(s):  
Ising Model ◽  
Curie Temperature ◽  
Small World ◽  
Small World Network ◽  
Real Network

The properties of 2D Ising model on a small world network are investigated. It is found that Curie temperature increases with the increase of small world links. The relations between the Curie temperature and the concentration of small world links are found. The possibility of using Ising model to describe real network is discussed.

scholarly journals Exact solution of Ising model on a small-world network

2004 ◽  
Vol 70 (2) ◽  
Author(s):  
J. Viana Lopes ◽  
Yu. G. Pogorelov ◽  
J. M. B. Lopes dos Santos ◽  
R. Toral
Keyword(s):  
Exact Solution ◽  
Ising Model ◽  
Small World ◽  
Small World Network

Zero-temperature ising spin dynamics on the homogeneous tree of degree three

2000 ◽  
Vol 37 (03) ◽  
pp. 736-747 ◽  
Author(s):  
C. Douglas Howard
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Spin Dynamics ◽  
Spin Chains ◽  
Homogeneous Tree ◽  
Zero Temperature ◽  
Spin Configuration ◽  
Ising Spin ◽  
Temperature Dynamics ◽  
Ferromagnetic Ising Model

We investigate zero-temperature dynamics for a homogeneous ferromagnetic Ising model on the homogeneous tree of degree three (𝕋) with random (i.i.d. Bernoulli) spin configuration at time 0. Letting θ denote the probability that any particular vertex has a +1 initial spin, for infinite spin clusters do not exist at time 0 but we show that infinite ‘spin chains’ (doubly infinite paths of vertices with a common spin) exist in abundance at any time ϵ > 0. We study the structure of the subgraph of 𝕋 generated by the vertices in time-ϵ spin chains. We show the existence of a phase transition in the sense that, for some critical θ c with spin chains almost surely never form for θ < θc but almost surely do form in finite time for θ > θc . We relate these results to certain quantities of physical interest, such as the t → ∞ asymptotics of the probability that any particular vertex changes spin after time t.

Zero-temperature ising spin dynamics on the homogeneous tree of degree three

2000 ◽  
Vol 37 (3) ◽  
pp. 736-747 ◽  
Author(s):  
C. Douglas Howard
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Spin Dynamics ◽  
Spin Chains ◽  
Homogeneous Tree ◽  
Zero Temperature ◽  
Spin Configuration ◽  
Ising Spin ◽  
Temperature Dynamics ◽  
Ferromagnetic Ising Model

We investigate zero-temperature dynamics for a homogeneous ferromagnetic Ising model on the homogeneous tree of degree three (𝕋) with random (i.i.d. Bernoulli) spin configuration at time 0. Letting θ denote the probability that any particular vertex has a +1 initial spin, for infinite spin clusters do not exist at time 0 but we show that infinite ‘spin chains’ (doubly infinite paths of vertices with a common spin) exist in abundance at any time ϵ > 0. We study the structure of the subgraph of 𝕋 generated by the vertices in time-ϵ spin chains. We show the existence of a phase transition in the sense that, for some critical θc with spin chains almost surely never form for θ < θc but almost surely do form in finite time for θ > θc. We relate these results to certain quantities of physical interest, such as the t → ∞ asymptotics of the probability that any particular vertex changes spin after time t.

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