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Homework Help: Magnetic Susceptibility (Ferromagnetic)

  1. Jun 13, 2009 #1
    1. The problem statement, all variables and given/known data
    Near the critical point, Gibbs free energy of a ferromagnetic system can be written as (1).
    a)Using the definition of magnetization, (2), show that

    [tex]m(t,H=0) = Bt^{\beta}[/tex]

    B is a constant. Determine [tex]\beta[/tex] in relation to [tex]\alpha[/tex] and [tex]\Delta[/tex]

    b) Show that the susceptibility when H = 0 can be written as

    [tex] \chi (t, H=0) = Ct^{-\gamma}[/tex]

    in which C is a constant. What is the relation between [tex]\gamma[/tex], [tex]\alpha[/tex] and [tex]\Delta[/tex]?

    2. Relevant equations
    [tex](1) \text{ } g(t,H) = t^{2-\alpha}F\left(\frac{T}{t^{\Delta}}\right)[/tex]

    [tex](2 ) m (t,H) = - \left(\frac{\partial g}{\partial H}\right)_T[/tex]

    t = (T - Tc)/Tc
    T = Temperature
    Tc = critical temperature
    H = magnetic field
    F(x) is a function
    g is gibbs free energy

    3. The attempt at a solution
    I've done item a, but I do not know what is the definition for the susceptibility of a ferromagnetic system.
    Last edited: Jun 13, 2009
  2. jcsd
  3. Apr 9, 2010 #2


    User Avatar

    Hi there, I am taking a grad level statmech course right now. The definition of magnetic susceptibility, regardless of the type of interaction (ferromagnetic or antiferromagnetic), is dm/dH.

    Above, m is the magnetization and H is the magnetic field.

    Hope that helps!
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