Answer Happy

We have a system of N distinguishable non-interacting spins in a magnetic field H. Each spin has a magnetic moment of size fl, and each can point either parallel or antiparallel to the field. Thus, the energy of a particular state is – MH, where the total magnetization M is given by N Μ = Σσιμ, di = £1, where Oil is the magnetic moment in the direction of the field. a) Using the microcanonical ensemble calculate the probability for a single spin be in the direction o, Po). Show that this probability can be written as P(0) = Ce-Belo), where C is a normalization constant and e(0) = -Huo is the energy per spin with direction o. Using the microcanonical ensemble calculate the joint probability that any two spins are in the directions 01, 02, P(01,02). Then calculate the covariance, cov(01,02) = (0102) – (01)(02). Discuss the thermodynamic limit, N +0. b)