https://doi.org/10.1140/epjb/e2005-00337-6
Zero temperature dynamics of Ising model on a densely connected small world network
Department of Physics, University of Calcutta,
92 Acharya Prafulla Chandra Road, Kolkata 700009, India
Corresponding author: a psphy@caluniv.ac.in
Received:
31
March
2005
Revised:
1
July
2005
Published online:
28
October
2005
The zero temperature quenching dynamics of the ferromagnetic Ising model
on a densely connected small world network is studied where long range
bonds are added randomly with a finite probability p. We find that in
contrast to the sparsely
connected networks and random graph, there is no freezing and
an initial random configuration
of the spins reaches the equilibrium
configuration within a very few Monte Carlo time steps
in the thermodynamic limit for any 
.
The residual energy and the number of spins flipped at any time shows an
exponential relaxation to equilibrium.
The persistence probability is also studied and it shows a saturation
within a few time
steps, the saturation value being 0.5 in the thermodynamic limit.
These results are explained in the light of the topological properties
of the network which is highly clustered and has a novel
small world behaviour.
PACS: 89.75.-k – Complex systems
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005
