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Bounds of Integration for Random Oriented particle

  1. Jun 15, 2015 #1
    In the Stoner-Wohlfarth model, a uniaxial, non-interacting particle is cooled to very low temperature with no exposure to an external field. Therefore, the orientation of each particle is random, if you have a group of particles. In their paper, they integrate such that:
    [tex]\langle \cos (\Theta )\rangle =\int_0^{\frac{\pi }{2}} \sin (\Theta ) \cos (\Theta ) \, d\Theta[/tex]

    I am having a hard time understanding why they only integrate from 0 to pi over two, instead of 0 to pi. Can anyone shine any enlightenment on this?

    Attached Files:

  2. jcsd
  3. Jun 15, 2015 #2


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    A copy of the paper can be found at http://spin.nanophys.kth.se/spin/stoner-wohlfarth.pdf There's a lot of discussion around Fig. 4 where they talk about how the symmetries of the problem allow them to reproduce the solutions everywhere in parameter space from the region ##0 \leq \theta,\phi \leq \pi/2##.
  4. Jun 16, 2015 #3
    That helped me tremendously - thank you!
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