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Homework Help: Feromagnet question

  1. Aug 6, 2010 #1
    1. The problem statement, all variables and given/known data
    How from





    [tex]G_{f,f'}(\omega)=\frac{1}{N}\sum_{\vec{q}} e^{i\vec{q}(\vec{f}-\vec{f'})}G_{\vec{q}}(\omega)[/tex]


    2. Relevant equations

    3. The attempt at a solution

    I really don't have a clue what to do. [tex]h[/tex] is constant.

    If I use that spin don't depands of indices


    and use

    [tex](\hbar\omega-h)\frac{1}{N}\sum_{\vec{q}} e^{i\vec{q}(\vec{f}-\vec{f'})}G_{\vec{q}}(\omega)=i2S\sigma\frac{1}{N}\sum_{q}e^{i\vec{q}(\vec{f}-\vec{f'})}+S\sigma\sum_gI(f-g)\{\frac{1}{N}\sum_{\vec{q}} e^{i\vec{q}(\vec{f}-\vec{f'})}G_{\vec{q}}(\omega)-\frac{1}{N}\sum_{\vec{q}} e^{i\vec{q}(\vec{g}-\vec{f'})}G_{\vec{q}}(\omega)\}[/tex]

    What now?
    Last edited: Aug 6, 2010
  2. jcsd
  3. Aug 6, 2010 #2


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    What is the definition of I(f-g) ? We need that to make any progress.
  4. Aug 6, 2010 #3
    [tex]I[/tex] is exchange interraction!

    [tex]\sum_f I(f)e^{-i\vec{g}\cdot\vec{f}}=J(\vec{q})[/tex]

    [tex]\sum_g I(f-g)=\sum_{\vec{\lambda}}I(\vec{\lambda})=J(0)\equiv J_0[/tex]
  5. Aug 8, 2010 #4
    Any idea?
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