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2 results

  • 10 - Phase Transitions and Order

  • Malcolm P. Kennett, Simon Fraser University, British Columbia
  • Book:
    Essential Statistical Physics
    Published online:
    29 August 2020
    Print publication:
    16 July 2020, pp 190-221

  • Summary

    Many different phases of matter can be characterized by the symmetries that they break.The Ising model for interacting spins illustrates this idea.In the absence of a magnetic field, there is a critical temperature, below which there is ferromagnetic ordering, and above which there is not.The magnetization is the order parameter for this transition: it is non-zero only when there is ferromagnetic ordering.The ferromagnetic phase transition in the Ising model is explored using the approximate method of mean field theory.Exact solutions are known for the Ising model in one and two dimensions and are discussed, along with numerical solutions using Monte Carlo simulations.Finally, the ideas of broken symmetry and their relationship to phase transitions are placed in the general framework of Landau theory and compared to results from mean field theory.

  • Can Mean Helicity Fluctuations Explain the Variability of the Solar Cycle ?

  • P. Hoyng
  • Journal:
    Symposium - International Astronomical Union / Volume 157 / 1993
    Published online by Cambridge University Press:
    19 July 2016, pp. 71-75
    Print publication:
    1993
    • Article
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  • I consider the effect of rapid fluctuations in the mean helicity on a plane dynamo wave in the αω-approximation and in the weak forcing limit. The phase shift and the logarithmic amplitude of the wave exhibit a correlated random walk, so that weaker (stronger) cycles last longer (shorter). The solar cycle data follow this prediction rather well. Mean helicity fluctuations are concluded to be an important source of solar cycle variability.