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

TL;DR

This study explores how different types of randomness in complex networks influence the zero-temperature quenching dynamics of the Ising model, revealing that both types lead to system freezing with subtle differences.

Contribution

It introduces and compares two models of randomness in networks and analyzes their effects on Ising model dynamics at zero temperature.

Findings

Both models cause the system to freeze in disordered states.

Maximum disorder occurs at specific parameters in each model.

Physical quantities show similar behavior with subtle differences.

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.