3. Consider a system consisting of N spin- particles, each of which can be in one of two quantum states, 'up' and 'down'. In a magnetic field B, the energy of a spin in the up/down state is tuB/2 where p is the magnetic moment. Show that the partition function is Z= 2 cosh Find the average energy E and entropy S. Check that your results for both quantities make sense in at T=0 and T> . Compute the magnetisation of the system, defined by M = N - N where N1/1 are the number of up/down spins. The magnetic susceptibility is defined as x = OM/OB. Derive Curie's Law which states that at high temperatures x~1/T.