Effect of the nature of randomness on quenching dynamics of Ising model on complex networks

Abstract

Randomness is known to affect the dynamical behaviour of many systems to a large extent. In this paper we investigate how the nature of randomness affects the dynamics in a zero temperature quench of Ising model on two types of random networks. In both the networks, which are embedded in a one dimensional space, the first neighbour connections exist and the average degree is four per node. In the random model A, the second neighbour connections are rewired with a probability $p$ while in the random model B, additional connections between neighbours at Euclidean distance $l(l>1)$ are introduced with a probability $P(l)\propto l^{-\alpha }$. We find that for both models, the dynamics leads to freezing such that the system gets locked in a disordered state. The point at which the disorder of the nonequilibrium steady state is maximum is located. Behaviour of dynamical quantities like residual energy, order parameter and persistence are discussed and compared. Overall, the behaviour of physical quantities are similar although subtle differences are observed due to the difference in the nature of randomness.

9 pages, 12 figures, written in revtex4 format, Published version of PRE

References in corpus (3)

• Phase transitions in Ising model on a Euclidean network
• Phase transition of a one-dimensional Ising model with distance-dependent connections
• Complex Networks: effect of subtle changes in nature of randomness

Cited by in corpus (10)

• Evolutionary potential games on lattices
• Long route to consensus: Two stage coarsening in a binary choice voting model
• Susceptible-Infected-Recovered model on Euclidean network
• Non-equilibrium dynamics in a three state opinion formation model with stochastic extreme switches
• Order-disorder transition in the zero-temperature Ising model on random graphs
• Stochastic Bifurcations in the Nonlinear Parallel Ising Model
• 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
• Active-absorbing phase transition and small world behaviour in Ising model on finite addition type networks in two dimensions