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

Federico Corberi, Alessandro Iannone, Manoj Kumar, Eugenio Lippiello, Paolo Politi

SciPost Phys. 10, 109 (2021) · published 18 May 2021

Abstract

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 rα. For α=0, i.e. mean field, all spins evolve coherently quickly driving the system towards a magnetised state. In the weak long range regime with α>1 there is a coarsening behaviour with competing domains of opposite sign without development of magnetisation. For strong long range, i.e. 0<α<1, we show that the system shows both features, with probability Pα(N) of having the latter one, with the different limiting behaviours limNPα(N)=0 (at fixed α<1) and limα1Pα(N)=1 (at fixed finite N). {\color{red}We discuss how this behaviour is a manifestation of an underlying dynamical scaling symmetry due to the presence of a single characteristic time τα(N)Nα.

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