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Self-averaging in the random two-dimensional Ising ferromagnet.

Victor Dotsenko1,2, Yurij Holovatch3,4, Maxym Dudka3,4

  • 1LPTMC, Université Paris VI, 75252 Paris, France.

Physical Review. E
|April 19, 2017
PubMed
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This study investigates fluctuations in a critical 2D Ising model with random couplings. Results show internal energy fluctuations scale with system size, while specific heat remains self-averaging.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Disordered Systems

Background:

  • Critical phenomena in disordered magnetic systems present unique theoretical challenges.
  • Understanding sample-to-sample fluctuations is crucial for interpreting experimental and simulation data.
  • Previous studies indicated a lack of self-averaging for certain quantities like free energy.

Purpose of the Study:

  • To analyze sample-to-sample fluctuations in critical two-dimensional Ising models with quenched disorder.
  • To derive explicit expressions for the probability distribution of critical internal energy and specific heat fluctuations.
  • To investigate the system size scaling of these fluctuations and their self-averaging properties.

Main Methods:

  • Utilized replica calculations within the renormalization group framework.

Related Experiment Videos

  • Derived analytical expressions for the probability distribution functions.
  • Analyzed the behavior of internal energy and specific heat distributions in the thermodynamic limit.

    • Main Results:

    • The probability distribution of critical internal energy was found to be Gaussian.
    • Typical sample-to-sample fluctuations and average internal energy scale as ∼Llnln(L) with system size L.
    • Specific heat was shown to be self-averaging, with its distribution converging to a delta peak as L approaches infinity.

    Conclusions:

    • The study provides direct, measurable insights into fluctuations in disordered Ising models.
    • Obtained results contrast with previous findings on the lack of self-averaging for free energy.
    • The findings have implications for interpreting measurements in real lattice systems and simulations.