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Nonuniversal behavior for aperiodic interactions within a mean-field approximation.

Maicon S Faria1, N S Branco, M H R Tragtenberg

  • 1Departamento de Física, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, Santa Catarina, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 4, 2008
PubMed
Summary
This summary is machine-generated.

This study explores the spin-1/2 Ising model on a Bethe lattice using aperiodic sequences. It reveals that mean-field methods can yield nonclassical critical exponents, challenging traditional assumptions.

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Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Aperiodic systems

Background:

  • The spin-1/2 Ising model is a fundamental model in statistical mechanics.
  • Bethe lattice provides a tractable framework for studying complex systems.
  • Aperiodic sequences introduce novel interactions in physical models.

Purpose of the Study:

  • To investigate the impact of deterministic aperiodic sequences on the critical behavior of the spin-1/2 Ising model.
  • To calculate exact critical temperatures and critical exponents for Fibonacci and period-doubling sequences.
  • To determine if mean-field approximations can lead to nonclassical critical exponents.

Main Methods:

  • Mean-field approximation applied to the spin-1/2 Ising model on a Bethe lattice.
  • Implementation of new algorithms for generating long deterministic aperiodic sequences (Fibonacci and period-doubling).
  • Exact calculation of critical temperature and critical exponents (beta, gamma, delta).

Main Results:

  • Classical critical exponents were found for the Fibonacci sequence.
  • For the period-doubling sequence, critical exponents depend on the ratio of exchange constants.
  • The standard relations between critical exponents hold for the period-doubling sequence within error margins.

Conclusions:

  • Mean-field-like procedures can produce nonclassical critical exponents.
  • Aperiodic sequences can lead to complex critical phenomena not observed in regular lattices.
  • The study highlights the importance of sequence properties in determining system behavior.