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Landau theory: why does a m^3 term implies first order transition phase

  1. Dec 7, 2011 #1

    I am not sure it is the right subcategory to post a question on statistical physics. But anyway, I read a couple of times that adding a m^3 to the Landau free energy implies that we may observe a first order transition phase, but I don't see why. Maybe it does imply some discontinuity in the entropy, latent heat, but I am not seeing that.
  2. jcsd
  3. Dec 8, 2011 #2


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    What is m? Mass, magnetic moment?
  4. Dec 10, 2011 #3
    M is the magnetic moment, the order parameter.
  5. Dec 11, 2011 #4
    Try to make a plot of a sample free energy:
    [itex]F=t m^2 + b m^3 + m^4[/itex]
    for different values of t and b? In particular, try a fixed t at some finite value and varies b.

    When t >> b, the free energy is minimum is at m=0, then as you increase b, at some point, the minimum JUMPS from 0 to some finite value. That, by definition, is a first order transition where the order parameter has a discontinuous jump.
  6. Dec 13, 2011 #5
    Thanks, you made it clear ;)
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