Novel Dynamical Phenomena in Magnetic systems

TL;DR

This thesis explores the zero-temperature quenching dynamics of Ising models with various complexities and introduces a novel opinion dynamics model linked to magnetic systems, revealing new phenomena in disordered and complex networks.

Contribution

It presents new insights into the effects of disorder and network complexity on Ising model dynamics and proposes a novel opinion model with phase transition behavior.

Findings

Discovered heterogeneity transition at a critical rigidity parameter.

Observed macroscopic crossover in opinion dynamics with size sensitivity.

Analyzed the impact of randomness on Ising models in complex networks.

Abstract

Dynamics of Ising models is a much studied phenomenon and has emerged as a rich field of present-day research. An important dynamical feature commonly studied is the quenching phenomenon below the critical temperature. In this thesis we have studied the zero temperature quenching dynamics of different Ising spin systems. First we have studied the zero temperature quenching dynamics of two dimensional Ising spin system with competating interactions. Then we have studied the effect of randomness or disorder on the quenching dynamics of Ising spin system. We have studied the effect of the nature of randomness on zero temperature quenching dynamics of one dimensional Ising model on two type of complex networks. A model for opinion dynamics also has been proposed in this thesis, in which the binary opinions of the individuals are determined according to the size of their neighboring domains. This model can be equivalently defined in terms of Ising spin variables and the various quantities studied have one to one correspondence with magnetic systems. Introducing disorder in this model through a parameter called rigidity parameter $\rho$ (probability that people are completely rigid and never change their opinion), the transition to a heterogeneous society at $\rho = 0^{+}$ is obtained. The Model (Model I) has been generalized introducing a parameter named as size sensitivity parameter to modify the dynamics of the proposed model and a macroscopic crossover in time is observed for the intermediate values of this parameter.