  We consider the two- (2D) and three-dimensional (3D) Ising model on a square
lattice at the critical temperature $T_c$, under Monte-Carlo spin flip
dynamics. The bulk magnetisation and the magnetisation of a tagged line in the
2D Ising model, and the bulk magnetisation and the magnetisation of a tagged
plane in the 3D Ising model exhibit anomalous diffusion. Specifically, their
mean-square displacement increases as power-laws in time, collectively denoted
as $\sim t^c$, where $c$ is the anomalous exponent. We argue that the anomalous
diffusion in all these quantities for the Ising model stems from time-dependent
restoring forces, decaying as power-laws in time --- also with exponent $c$ ---
in striking similarity to anomalous diffusion in polymeric systems. Prompted by
our previous work that has established a memory-kernel based Generalised
Langevin Equation (GLE) formulation for polymeric systems, we show that a
closely analogous GLE formulation holds for the Ising model as well. We obtain
the memory kernels from spin-spin correlation functions, and the formulation
allows us to consistently explain anomalous diffusion as well as anomalous
response of the Ising model to an externally applied magnetic field in a
consistent manner.
