# Magnetic Susceptibility (Ferromagnetic)

1. Jun 13, 2009

### sombrancelha

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

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

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 $$\Delta$$?

2. Relevant 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 - 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. Apr 9, 2010

### 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!