Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Feromagnet question

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

    [tex](\hbar\omega-h)G_{f,f'}(\omega)=i2\langle\hat{S}_f^z\rangle\delta_{f,f'}+\langle\hat{S}^z\rangle\sum_gI(f-g)\{G_{f,f'}(\omega)-G_{g,f'}(\omega)\}[/tex]

    get

    [tex]G_{q}(\omega)=\frac{i\hbar}{2\pi}\frac{2\langle\hat{S}^z\rangle}{\hbar\omega-h-\epsilon(q)}[/tex]

    where

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

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

    [tex]\langle\hat{S}^z\rangle=\langle\hat{S}_g^z\rangle=S\sigma[/tex]

    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

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member


    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?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook