Consider a paramagnetic material where the magnetic moments may take three values, +μ, -μ and 0. In a magnetic field B, the associated energies are, respectively, -μB, +μB and 0. There are N independent spins in the sample.
(a) Compute the partition function for this system as a function of N, T and B.
(b) Compute the average energy of the system.
(c) Compute the average magnetization of the system.