Problem 6 (12 marks) Consider a paramagnet made of / spin-1/2 magnetic moments # in thermal equilibrium at temperature 7. Let the energy of a single magnetic moment be E = -Bus, where 5 = #1 denotes the value of the spin and B is the strength of the applied magnetic field. Determine the average magnetization (M) and the average of the square of the magnetization (M2). Compute the standard deviation of = (M2) - (M)? and compute vow /(M). How does this ratio behave in the large- N limit? Explain the significance of your finding