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
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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−α. 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 limN→∞Pα(N)=0 (at fixed α<1) and limα→1Pα(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.
Cited by 9

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