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Critical fluctuations of time-dependent magnetization in a random-field Ising model

Hiroki Ohta1, Shin-Ichi Sasa

  • 1Department of Pure and Applied Sciences, University of Tokyo, Japan. hiroki@jiro.c.u-tokyo.ac.jp

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 21, 2008
PubMed

Insights

Researchers studied cooperative behaviors near critical points in a random-field Ising model. They found that magnetization fluctuations and characteristic length scales diverge near these points, indicating critical phenomena.

Area of Science:

  • Physics
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Disorder-induced phase transitions are crucial in understanding complex systems.
  • The random-field Ising model provides a framework for studying such transitions.
  • Cooperative behaviors near critical points are key to understanding emergent properties.

Purpose of the Study:

  • To numerically investigate cooperative behaviors near disorder-induced critical points.
  • To analyze the dynamics of ordering processes in the random-field Ising model.
  • To characterize the critical exponents associated with these phenomena.

Main Methods:

  • Numerical investigation of the random-field Ising model.
  • Analysis of time-dependent magnetization during ordering processes.
  • Application of finite-size scaling methods to estimate critical exponents.

Main Results:

  • Fluctuations in time-dependent magnetization, chi(t), show a maximum at time tau.
  • Both chi(tau) and tau diverge near the disorder-induced critical point.
  • A characteristic length scale also diverges near the critical point, characterizing spin configurations.

Conclusions:

  • Cooperative behaviors manifest as divergences in magnetization fluctuations and length scales near the critical point.
  • The study provides estimates for critical exponents characterizing these power-law divergences.
  • Numerical findings offer insights into the nature of disorder-induced phase transitions.

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