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## 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

[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]?

## Homework 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 - 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.

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