## 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

- doi: 10.21468/SciPostPhys.10.5.109
- Submissions/Reports

### 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 $r^{-\alpha}$. For $\alpha =0$, i.e. mean field, all spins evolve coherently quickly driving the system towards a magnetised state. In the weak long range regime with $\alpha >1$ there is a coarsening behaviour with competing domains of opposite sign without development of magnetisation. For strong long range, i.e. $0<\alpha <1$, we show that the system shows both features, with probability $P_\alpha (N)$ of having the latter one, with the different limiting behaviours $\lim _{N\to \infty}P_\alpha (N)=0$ (at fixed $\alpha<1$) and $\lim _{\alpha \to 1}P_\alpha (N)=1$ (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 $\tau _\alpha (N)\sim N^\alpha$.

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Federico Corberi, -
^{2}Alessandro Iannone, -
^{3}Manoj Kumar, -
^{4}Eugenio Lippiello, -
^{5}^{6}Paolo Politi

^{1}Università degli Studi di Salerno / University of Salerno [UNISA]^{2}Università di Pisa / University of Pisa [UniPi]^{3}Coventry University^{4}Università degli Studi della Campania “Luigi Vanvitelli”^{5}Istituto Nazionale di Fisica Nucleare / National Institute for Nuclear Physics [INFN]^{6}Istituto dei sistemi complessi / Institute for Complex Systems [ISC]

- Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) (through Organization: Ministero dell'Istruzione, dell'Università e della Ricerca / Ministry of Education, Universities and Research [MIUR])
- Royal Society