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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
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Nature versus nurture: predictability in low-temperature Ising dynamics.

J Ye1, J Machta, C M Newman

  • 1Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA and Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544, USA.

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Summary
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Nature versus nurture in dynamical systems: Initial conditions significantly influence final states in the 2D Ising ferromagnet, with overlap decaying over time. This suggests a strong "heritability" from initial states in stochastic dynamics.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Dynamical many-body systems evolve from initial states via stochastic processes.
  • Understanding the balance between initial conditions (nature) and random dynamics (nurture) is crucial for predicting system outcomes.

Purpose of the Study:

  • To quantify the relative importance of initial state versus stochastic dynamics in determining the final state of a system.
  • To investigate the concept of "heritability" in the context of physical systems.

Main Methods:

  • Monte Carlo simulations were employed to study the two-dimensional Ising ferromagnet.
  • Simulations involved a deep quench from infinite temperature to zero (or low non-zero) temperature.
  • The overlap between "identical twins" (systems with identical initial states but independent dynamics) was analyzed.

Main Results:

  • The overlap between identical twins decays with time as t(-θ)(h).
  • The heritability exponent was found to be θ(h) = 0.22 ± 0.02.
  • This exponent remained consistent for quenches to both T=0 and low non-zero temperatures.

Conclusions:

  • The initial state plays a significant role in the long-term behavior of the 2D Ising ferromagnet under deep quench conditions.
  • The identified "heritability exponent" quantifies the influence of initial conditions on the system's evolution.
  • While potentially related, the heritability exponent may differ from the persistence exponent in more general cases.