  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.
