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Gaps between avalanches in one-dimensional random-field Ising models.

Jishnu N Nampoothiri1, Kabir Ramola1, Sanjib Sabhapandit2

  • 1Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA.

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|January 20, 2018
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Summary
This summary is machine-generated.

We analyzed avalanche gaps in random-field Ising models (RFIMs). For ferromagnetic RFIMs, gap distributions follow a Poisson process, while antiferromagnetic RFIMs show power-law behavior near the gap offset.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Disordered systems

Background:

  • Avalanches are critical phenomena observed in various systems.
  • Understanding avalanche statistics provides insights into system dynamics and phase transitions.
  • Random-field Ising models (RFIMs) are fundamental models for studying disorder effects.

Purpose of the Study:

  • To analyze the statistical properties of avalanche gaps in one-dimensional RFIMs at zero temperature.
  • To investigate the influence of disorder strength and range on avalanche gap distributions.
  • To compare analytical predictions with numerical simulations for different RFIMs.

Main Methods:

  • Analytical calculation of avalanche gap distributions using a nonhomogeneous Poisson process for ferromagnetic RFIMs.
  • Numerical simulations to verify analytical results and study long-range antiferromagnetic RFIMs.
  • Characterization of gap distributions near offset values using power-law analysis.

Main Results:

  • The avalanche gap distribution P(ΔH) for ferromagnetic RFIMs tends to a constant C(R) as ΔH→0+, showing nontrivial dependence on disorder R.
  • A gapped behavior P(ΔH)=0 is observed for antiferromagnetic RFIMs up to a system-size dependent offset ΔH_{off}.
  • The gap distribution for antiferromagnetic RFIMs follows P(ΔH)∼(ΔH-ΔH_{off})^{θ} with θ≈0.95(5).

Conclusions:

  • The study provides a comprehensive analysis of avalanche gap statistics in different RFIMs.
  • Analytical and numerical findings reveal distinct behaviors for ferromagnetic and antiferromagnetic RFIMs.
  • The results offer insights into the role of quenched disorder and interaction range in critical phenomena.