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

Abstract

Randomness is known to affect the dynamical behavior 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 the Ising model on two types of random networks. In both networks, which are embedded in a one-dimensional space, the first-neighbor connections exist and the average degree is 4 per node. In random model A the second-neighbor connections are rewired with a probability p, while in random model B additional connections between neighbors at a Euclidean distance l(l > 1) are introduced with a probability P(l) proportionally l(-α). 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. The behavior of dynamical quantities such as residual energy, order parameter, and persistence are discussed and compared. Overall, the behavior of physical quantities are similar, although subtle differences are observed due to the difference in the nature of randomness.

Evolutionary potential games on lattices

“…8.1. Evolution in the limit K → 0 The pattern evolution in the Ising model on different lattices and graphs has been studied for several years in the zero noise limit [292]. This particular case exhibits some curiosity.…”

“…Recently Biswas and Sen [292] have studied the Ising system on a random network created from the one-dimensional lattice by adding new links into the connectivity structure. As a result the lattice sites have different degrees and for some constellations these irregularities were capable of blocking the domain growing processes, independently of the details of the generation of random networks.…”

Stochastic bifurcations in the nonlinear parallel Ising model

“…The Ising model has been studied in different topologies [31][32][33][34], in particular, the topological details may affect the critical dynamics [35] and the zero-temperature quench [36].…”

Zero temperature ordering dynamics in two dimensional BNNNI model

“…The presence of domain walls in regular lattices causes an energy cost [14]. It have been shown before for the two dimensional Ising model that the residual energy have same scaling as that of the number or fraction of domain walls [15,20]…”

“…To study the effect of the competing interaction on the dynamical behaviour, the simple Ising model with a competing next nearest neighbor interaction has been studied earlier in both one and two dimensions [11][12][13]16]. Competing interactions could also be present in the system if spins have random long range interactions which are quenched in nature [14,15].…”