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We consider the two- (2D) and three-dimensional (3D) Ising model on a squarelattice at the critical temperature $T_c$, under Monte-Carlo spin flipdynamics. The bulk magnetisation and the magnetisation of a tagged line in the2D Ising model, and the bulk magnetisation and the magnetisation of a taggedplane in the 3D Ising model exhibit anomalous diffusion. Specifically, theirmean-square displacement increases as power-laws in time, collectively denotedas $\sim t^c$, where $c$ is the anomalous exponent. We argue that the anomalousdiffusion in all these quantities for the Ising model stems from time-dependentrestoring forces, decaying as power-laws in time --- also with exponent $c$ ---in striking similarity to anomalous diffusion in polymeric systems. Prompted byour previous work that has established a memory-kernel based GeneralisedLangevin Equation (GLE) formulation for polymeric systems, we show that aclosely analogous GLE formulation holds for the Ising model as well. We obtainthe memory kernels from spin-spin correlation functions, and the formulationallows us to consistently explain anomalous diffusion as well as anomalousresponse of the Ising model to an externally applied magnetic field in aconsistent manner.

Generalised Langevin Equation Formulation for Anomalous Diffusion in the Ising Model at the Critical Temperature