Applying the grand canonical ensemble to a magnetic system

[mondeo2015]

Homework Statement

Consider a system with N sites and N particles with magnetic moment m. Each site can be in one of three states: empty with energy 0, occupied by one particle with energy 0 (in the absent of magnetic field) or occupied by two particles with anti parallel moments and energy ε. The system is placed in a magnetic field B, acting on the magnetic moment of the particles. Assume that two particles in the same site are indistinguishable.

a. We are to find the chemical potential of the system μ. Hint: we should use <N>=N as seen in class.

b. We are to find the mean energy of the system <E>.

Homework Equations

The usual grand canonical ensemble. The basics of paramagnetism law of total energy.

The Attempt at a Solution

I figured the idea was to apply the grand canonical ensemble but the technicalities are beyond my ability to approach so I am unsure of whether or not the grand canonical ensemble is the idea here. I truly need help and thank all helpers.