Nature Versus Nurture: Dynamical Evolution in Disordered Ising Ferromagnets

Lily Z. Wang, Reza Gheissari, Charles M. Newman, Daniel L. Stein

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the predictability of zero-temperature Glauber dynamics in various models of disordered ferromagnets. This is analyzed using two independent dynamical realizations with the same random initialization (called twins). We derive, theoretically and numerically, trajectories for the evolution of the normalized magnetization and twin overlap as the system size tends to infinity. The systems we treat include mean-field ferromagnets with light-tailed and heavy-tailed coupling distributions, as well as highly-disordered models with a variety of other geometries. In the mean-field setting with light-tailed couplings, the disorder averages out and the limiting trajectories of the magnetization and twin overlap match those of the homogenous Curie–Weiss model. On the other hand, when the coupling distribution has heavy tails, or the geometry changes, the effect of the disorder persists in the thermodynamic limit. Nonetheless, qualitatively all such random ferromagnets share a similar time evolution for their twin overlap, wherein the two twins initially decorrelate, before either partially or fully converging back together due to the ferromagnetic drift.

Original languageEnglish (US)
Title of host publicationStatistical Mechanics of Classical and Disordered Systems, StaMeClaDys 2018
EditorsVéronique Gayrard, Louis-Pierre Arguin, Nicola Kistler, Irina Kourkova
PublisherSpringer
Pages215-237
Number of pages23
ISBN (Print)9783030290764
DOIs
StatePublished - 2019
EventInternational Conference on Statistical Mechanics of Classical and Disordered Systems, StaMeClaDys 2018 - Marseille, France
Duration: Aug 27 2018Aug 31 2018

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume293
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceInternational Conference on Statistical Mechanics of Classical and Disordered Systems, StaMeClaDys 2018
CountryFrance
CityMarseille
Period8/27/188/31/18

Keywords

  • Curie–Weiss model
  • Glauber dynamics
  • Predictability
  • Random ferromagnet
  • Spin glass

ASJC Scopus subject areas

  • Mathematics(all)

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