Question

A statistical system is composed of N particles with spin 1 2 , immersed in a magnetic field H. The particles are fixed in their positions and possess a magnetic moment µ. The Hamiltonian of such a system is H = −µH X N i=1 σi where σi = ±1

(a) Given that the separation between the spins in the lattice is larger than their de Broglie wavelength, should the spins be treated as distinguishable or indistinguishable particles?

(b) Write down the canonical partition function, QN , for the N particles.

(c) Determine the total energy for this system at an arbitrary temperature, T.

(d) Magnetization is defined as the M = µ(N+ − N−) where N+ and N− are the average number of up and down spins, respectively. Determine M for a given temperature T.

(e) The susceptibility is defined as χ = ∂M ∂H T Find the small magnetic field limit of the susceptibility

Answer 1

These are four options.

As magnetization is given , the differentiation of it with respect to H will give the susceptibility, and from that limit on susceptibility can be found.