Magnetic Susceptibility (Ferromagnetic)

[sombrancelha]

Homework Statement

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

$$m(t,H=0) = Bt^{\beta}$$

B is a constant. Determine $$\beta$$ in relation to $$\alpha$$ and $$\Delta$$

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

$$\chi (t, H=0) = Ct^{-\gamma}$$

in which C is a constant. What is the relation between $$\gamma$$, $$\alpha$$ and $$\Delta$$?

Homework Equations

$$(1) \text{ } g(t,H) = t^{2-\alpha}F\left(\frac{T}{t^{\Delta}}\right)$$

$$(2 ) m (t,H) = - \left(\frac{\partial g}{\partial H}\right)_T$$

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

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.

 

[JGS]

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!