Universal behavior in finite 2D kinetic ferromagnets

Research output: Working paper

Abstract

We show that quenching and coarsening of the kinetic Ising model with a non-conserved order parameter displays the same average evolution for finite systems of arbitrary size. This multiscale similarity applies not just within the characteristic length scale of the system, but also at all length and time scales, including in the regime where simple dynamical scaling fails for finite systems. As a consequence, beyond rapidly decaying finite size effects, the evolution of correlations in small systems exactly parallels arbitrarily larger cases. We suggest that dynamical scaling data collapse can be partially restored with an area law-like correction, but unlike the multiscale behavior, this does not hold for distances approaching a quarter of the system size.
LanguageEnglish
Place of PublicationIthaca, N.Y.
Number of pages5
Publication statusPublished - 25 Sep 2018

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kinetics
scaling
Ising model
quenching

Keywords

  • coarsening
  • universal behaviour
  • ising model

Cite this

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title = "Universal behavior in finite 2D kinetic ferromagnets",
abstract = "We show that quenching and coarsening of the kinetic Ising model with a non-conserved order parameter displays the same average evolution for finite systems of arbitrary size. This multiscale similarity applies not just within the characteristic length scale of the system, but also at all length and time scales, including in the regime where simple dynamical scaling fails for finite systems. As a consequence, beyond rapidly decaying finite size effects, the evolution of correlations in small systems exactly parallels arbitrarily larger cases. We suggest that dynamical scaling data collapse can be partially restored with an area law-like correction, but unlike the multiscale behavior, this does not hold for distances approaching a quarter of the system size.",
keywords = "coarsening, universal behaviour, ising model",
author = "James Denholm and Ben Hourahine",
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TY - UNPB

T1 - Universal behavior in finite 2D kinetic ferromagnets

AU - Denholm, James

AU - Hourahine, Ben

PY - 2018/9/25

Y1 - 2018/9/25

N2 - We show that quenching and coarsening of the kinetic Ising model with a non-conserved order parameter displays the same average evolution for finite systems of arbitrary size. This multiscale similarity applies not just within the characteristic length scale of the system, but also at all length and time scales, including in the regime where simple dynamical scaling fails for finite systems. As a consequence, beyond rapidly decaying finite size effects, the evolution of correlations in small systems exactly parallels arbitrarily larger cases. We suggest that dynamical scaling data collapse can be partially restored with an area law-like correction, but unlike the multiscale behavior, this does not hold for distances approaching a quarter of the system size.

AB - We show that quenching and coarsening of the kinetic Ising model with a non-conserved order parameter displays the same average evolution for finite systems of arbitrary size. This multiscale similarity applies not just within the characteristic length scale of the system, but also at all length and time scales, including in the regime where simple dynamical scaling fails for finite systems. As a consequence, beyond rapidly decaying finite size effects, the evolution of correlations in small systems exactly parallels arbitrarily larger cases. We suggest that dynamical scaling data collapse can be partially restored with an area law-like correction, but unlike the multiscale behavior, this does not hold for distances approaching a quarter of the system size.

KW - coarsening

KW - universal behaviour

KW - ising model

UR - https://arxiv.org/abs/1809.09523v1

M3 - Working paper

BT - Universal behavior in finite 2D kinetic ferromagnets

CY - Ithaca, N.Y.

ER -