This homework assignment is optional. Its focus is on the nature of the magnetic susceptibility close to a phase transition from a paramagnetic state to a state with spontaneous magnetization.
1. Using the model of free energy of a metal which exhibits spontaneous magnetization* below a characteristic temperature Tc (as we discussed in class today) calculate the magnetic susceptibility in the normal metal state, that is, above Tc. Show that it becomes quite large near Tc and graph it as a function of T for T greater than Tc. What is the nature of its divergence?
(Note: Taking advantage of the restriction to linear response simplifies your calculation significantly.)
*A value of U-Bandwidth of about 0.1 eV should be fine for this problem. What is Tc for this case?
notes: Magnetic susceptibility is defined in terms of linear response. You can add a term to your free energy associated with a small applied magnetic field, something like \(\mu_B B\), where this B is applied magnetic field (not bandwidth). The position of the minimum of F in the presence of non-zero applied magnetic field, B, will tell you the induced magnetization and the susceptibility.
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