A molecular crystal is consisted of N molecules which can be found in two forms, either form A with energy ε or form B with energy 0 when there's no external magnetic field. Situation B of each molecule has total spin of 1/2 (and correspondent magnetic bipolar moment equal - by absolute value - to μ), while the total spin for situation A is zero. Say that there is an implemented homogeneous magnetic field (along the z-axis) with intensity H, which means that there is a correspondent Zeeman energy-interraction for each molecule. We suppose that the molecules dont interract with each other.
a) Find the partition function of the system
b) Find the mean total energy of the crystal as a function of temperature (and the magnetic field H)
c) Find the magnetisation and the magnetic susceptibility of the crystal as a function of temperature (and the magnetic field H). Find the asymptotic behaviors of the magnetiasation (testing the different possibilities for the parameters of the problem) in very high and very low temperatures.