Coexistence of coarsening and mean field relaxation in the long-range Ising chain

We study the kinetics after a low temperature quench of the one-dimensional Ising model with long range interactions between spins at distance r decaying as r-?. For ? = 0, i.e. mean field, all spins evolve coherently quickly driving the system towards a magnetised state. In the weak long range regime with ? > 1 there is a coarsening behaviour with competing domains of opposite sign without development of magnetisation. For strong long range, i.e. 0 < ? < 1, we show that the system shows both features, with probability P?(N) of having the latter one, with the different limiting behaviours limN->? P?(N) = 0 (at fixed ? < 1) and lim?->1 P?(N) = 1 (at fixed finite N). We discuss how this behaviour is a manifestation of an underlying dynamical scaling symmetry due to the presence of a single characteristic time ??(N) ~ N?. Copyright © F. Corberi et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.