Coexistence of coarsening and mean field relaxation in the long-range Ising chain
Federico Corberi, Alessandro Iannone, Manoj Kumar +2 more
We study the kinetics after a low temperature quench of the one-dimensional Ising model with long range interactions between spins at distance r r decaying as r^{-\alpha} r − α . For \alpha =0 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 \alpha >1 α > 1 there is a coarsening behaviour with competing domains of opposite sign without development of magnetisation. For strong long range, i.e. 0<\alpha <1 0 < α < 1 , we show that the system shows both features, with probability P_\alpha (N) P α ( N ) of having the latter one, with the different limiting behaviours \lim _{N\to \infty}P_\alpha (N)=0 lim N → ∞ P α ( N ) = 0 (at fixed \alpha<1 α < 1 ) and \lim _{\alpha \to 1}P_\alpha (N)=1 lim α → 1 P α ( N ) = 1 (at fixed finite N N ). We discuss how this behaviour is a manifestation of an underlying dynamical scaling symmetry due to the presence of a single characteristic time \tau _\alpha (N)\sim N^\alpha τ α ( N ) ∼ N α .
arXiv:2102.08217•SciPost Physics•May 18, 2021•16 citations