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Geometry-induced nonequilibrium phase transition in sandpiles.

M N Najafi1, J Cheraghalizadeh1, M Luković2,3

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We identified two universality classes in a 3D sandpile model on Ising clusters, revealing a tricritical point. This transition is driven by changes in the cluster support, impacting avalanche behavior and critical exponents.

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Area of Science:

  • Complex Systems
  • Statistical Physics
  • Computational Physics

Background:

  • The sandpile model is a paradigm for self-organized criticality (SOC).
  • Ising clusters provide a complex support structure for studying critical phenomena.
  • Understanding universality classes and critical transitions is key in statistical physics.

Purpose of the Study:

  • To investigate the sandpile model on 3D spanning Ising clusters.
  • To analyze avalanche behavior and identify universality classes under temperature control.
  • To characterize the tricritical point and its associated critical exponents.

Main Methods:

  • Simulations of the 3D sandpile model on Ising clusters.
  • Analysis of 3D avalanches and their 2D projections.
  • Finite-size scaling analysis of various physical quantities.

Main Results:

  • Discovery of two universality classes: ordinary BTW and SOC_{T=∞}.
  • Identification of a tricritical point at T_{c}, the host's critical temperature.
  • Characterization of critical exponents for avalanche size distribution (τ^{T=∞}=1.27±0.03) and scaling behavior (β=0.19±0.02, ν=0.75±0.05).
  • The fractal dimension of avalanche perimeters is robust (D_{f}=1.25±0.01).

Conclusions:

  • The sandpile model on 3D Ising clusters exhibits rich critical behavior with distinct universality classes.
  • The transition between criticalities is induced by support changes, highlighting the role of the substrate.
  • The findings provide insights into SOC, critical phenomena, and their relation to amorphous ferromagnets.