Domain statistics in the relaxation of the 1D Ising model with long-range interactions in Chaos, Solitons and Fractals

ISC researcher Paolo Politi coauthored an interesting article published  in Chaos, Solitons and Fractals.
F. Corberi, M. Kumar, E. Lippiello and P. Politi, Domain statistics in the relaxation of the one-dimensional Ising model with strong long-range interactions, Chaos, Solitons and Fractals, 173,113681, (2023).

After a zero temperature quench, we study the kinetics of the one-dimensional Ising model with long-range interactions between spins at a distance r decaying as r^-α with α≤1. As shown in our recent study (Corberi et al., 2021) that only a fraction of the non-equilibrium trajectories is characterised by the presence of coarsening domains while in the remaining ones the system is quickly driven towards a magnetised state. Restricting to realisations displaying coarsening we compute numerically the probability distribution of the size of the domains and find that it exhibits a scaling behaviour with an unusual -dependent power-law decay. This peculiar behaviour is also related to the divergence of the average size of domains with system size at finite times. Such a scenario differs from the one observed when α>1 , where the distribution decays exponentially. Finally, based on numerical results and on analytical calculations we argue that the average domain size grows asymptotically linearly in time.