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Tricritical behavior in deterministic aperiodic ising systems

Haddad1, Ghosh, Salinas

  • 1Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP, Brazil.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|January 4, 2001
PubMed
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This study explores how geometric fluctuations in a mixed-spin model affect phase transitions. Aperiodic interactions weaken tricritical singularities, shifting them to lower temperatures and dimensions.

Area of Science:

  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • First-order phase transitions and tricritical phenomena are critical in understanding material properties.
  • Aperiodic systems introduce complex behaviors not seen in periodic counterparts.

Purpose of the Study:

  • Investigate the impact of deterministic geometric fluctuations on first-order transitions.
  • Analyze the effects of aperiodicity on tricritical phenomena in a mixed-spin model.

Main Methods:

  • Utilized a mixed-spin model with aperiodic ferromagnetic exchange interactions and crystalline fields.
  • Employed a Migdal-Kadanoff real-space renormalization-group calculation on a hierarchical lattice.

Main Results:

  • Demonstrated that aperiodicity qualitatively impacts tricritical and simple critical behavior similarly.

Related Experiment Videos

  • Showed the tricritical fixed point becomes unstable beyond a threshold dimension, replaced by a two-cycle.

    • Conclusions:

    • Aperiodicity weakens and depresses tricritical singularities in temperature and dimension.
    • Geometric fluctuations significantly alter critical phenomena in magnetic systems.