Let us consider a system of N spin-1/2 particles (see the previous problem) per unit volume in thermal equilibrium, in our external magnetic field B. Recall that the canonical distribution is:
ρ=Ze−H/T,(4.135)
with partition function:
Z=Tr(e−H/T).(4.136)
Such a system of particles will tend to orient along the magnetic field, resulting in a bulk magnetization (having units of magnetic moment per unit volume), M.
(a) Give an expression for this magnetization (don't work too hard to evaluate).
(b) What is the magnetization in the high-temperature limit, to lowest non-trivial order (this I want you to evaluate as completely as you can!)?