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

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

doi:10.21468/SciPostPhys.10.5.109

SciPost Physics

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 $r^{-\alpha}$. 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 $\tau _\alpha (N)\sim N^\alpha$.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.10.5.109
TI  - Coexistence of coarsening and mean field relaxation in the long-range Ising chain
PY  - 2021/05/18
UR  - https://www.scipost.org/SciPostPhys.10.5.109
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 10
IS  - 5
SP  - 109
A1  - Corberi, Federico
AU  - Iannone, Alessandro
AU  - Kumar, Manoj
AU  - Lippiello, Eugenio
AU  - Politi, Paolo
AB  - 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 $\tau _\alpha (N)\sim N^\alpha$.
ER  -

@Article{10.21468/SciPostPhys.10.5.109,
	title={{Coexistence of coarsening and mean field relaxation in the long-range Ising chain}},
	author={Federico Corberi and Alessandro Iannone and Manoj Kumar and Eugenio Lippiello and Paolo Politi},
	journal={SciPost Phys.},
	volume={10},
	pages={109},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.10.5.109},
	url={https://scipost.org/10.21468/SciPostPhys.10.5.109},
}

Cited by 9

Authors / Affiliations: mappings to Contributors and Organizations

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¹ Federico Corberi,
² Alessandro Iannone,
³ Manoj Kumar,
⁴ Eugenio Lippiello,
⁵ ⁶ Paolo Politi

Funders for the research work leading to this publication

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