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

Abstract

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 $p\ne 0$. 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.

Replaced by accepted version in Eur. Phys. J B

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Cited by in corpus (12)

• Evolutionary potential games on lattices
• The dynamic exponent of the Ising model on negatively curved surfaces
• Local Persistence in the Directed Percolation Universality Class
• Effect of the nature of randomness on quenching dynamics of Ising model on complex networks
• Zero-temperature dynamics in the dilute Curie-Weiss model
• Zero-temperature Glauber dynamics on small-world networks
• Susceptible-Infected-Recovered model on Euclidean network
• Order-disorder transition in the zero-temperature Ising model on random graphs
• Multidimensional persistence behaviour in an Ising system
• Frozen states and active-absorbing phase transitions of the Ising model on networks
• Phase transitions in Ising model induced by weight redistribution on weighted regular networks
• Zero temperature ordering dynamics in two dimensional BNNNI model