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G Muñoz-Gil1, C Charalambous1, M A García-March1

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This summary is machine-generated.

This study models particle diffusion on an Ising environment, revealing that particle diffusivity depends on local spin geometry. Anomalous diffusion and ergodicity breaking occur at critical temperatures, with transient subdiffusion observed otherwise.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Particle transport phenomena are fundamental in various scientific disciplines.
  • Understanding anomalous diffusion requires modeling complex interactions between particles and their environments.
  • Ising models provide a framework for studying emergent behavior in interacting systems.

Purpose of the Study:

  • To introduce a novel model of continuous-time random walk (CTRW) coupled to an Ising environment.
  • To investigate how local geometric properties of the Ising environment influence particle diffusivity.
  • To analyze the conditions leading to anomalous diffusion and ergodicity breaking.

Main Methods:

  • Development of a theoretical model combining CTRW with Ising dynamics.
  • Analysis of particle diffusivity as a function of local spin cluster sizes.
  • Investigation of system behavior at critical and non-critical temperatures.
  • Examination of ergodicity breaking at different timescales.

Main Results:

  • Particle diffusivity is locally modulated by the geometry of the Ising environment (connected spin clusters).
  • Anomalous diffusion and apparent ergodicity breaking are observed at the critical temperature.
  • Finite-size effects or deviations from criticality lead to transient subdiffusion, followed by normal diffusion.
  • The timescale for returning to normal diffusion depends on the limiting scale and proximity to criticality.

Conclusions:

  • The interplay between CTRW and Ising dynamics generates complex transport behaviors.
  • Anomalous diffusion and ergodicity breaking are hallmarks of criticality in this coupled system.
  • Finite environments and temperatures regularize the diffusion, leading to transient anomalous behavior.