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Griffiths phase in a three-dimensional Ising model with aperiodic interactions.

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|June 19, 2025
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Summary
This summary is machine-generated.

Simulations of a three-dimensional ferromagnetic Ising model reveal that increasing aperiodicity creates a Griffiths phase. This phase, characterized by divergent susceptibility, is linked to the wandering exponent and aperiodicity strength.

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Area of Science:

  • Condensed matter physics
  • Statistical mechanics
  • Magnetism

Background:

  • The ferromagnetic Ising model is a fundamental model in statistical mechanics.
  • Understanding the effects of disorder and aperiodicity on magnetic systems is crucial.
  • Previous studies have explored these effects in lower dimensions or with different types of disorder.

Purpose of the Study:

  • To investigate the impact of aperiodicity on a three-dimensional ferromagnetic Ising model.
  • To identify the conditions under which a Griffiths phase emerges.
  • To explore the relationship between Griffiths phase characteristics and system parameters.

Main Methods:

  • Three-dimensional ferromagnetic Ising model simulation.
  • Monte Carlo simulation techniques.
  • Analysis of heat capacity and magnetic susceptibility.

Main Results:

  • Weak aperiodicity leads to behavior similar to pure systems.
  • Increasing aperiodicity (controlled by 'r') induces a multipeak structure in heat capacity.
  • A region of divergent susceptibility, indicative of a Griffiths phase, was observed for marginal and relevant sequences.
  • The extent of the Griffiths phase correlates with the wandering exponent and aperiodicity strength.

Conclusions:

  • Aperiodic interactions can induce a Griffiths phase in a 3D Ising model.
  • The Griffiths phase is a hallmark of systems with quenched disorder.
  • The study provides insights into the critical behavior of disordered magnetic systems.