A Guide to Physics Problems. Part 2. Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 41

Derive expressions for the

Partitionfunction

Average spin

Internalenergy

4.85 N Independent Spins (Tennessee)

Consider a system of N independent spin-1/2 particles. In a magnetic field

H, in the direction, they can point either up or down with energy

where is the magnetic moment.Deriveexpressions for the

Partitionfunction

Internal energy

Entropy

4.86 NIndependent Spins, Revisited (Tennessee)

Consider a system of N independent spin-1/2 particles. In a magnetic field
H, in the direction, they can point either up or down with energy
where is the magneticmoment and Deriveexpressions for the
entropy in the case of a microcanonical ensemble, where the number
of particles N and the magnetization are fixed.

4.87 Ferromagnetism (Maryland, MIT)

The spins of a regular Ising lattice interact by the energy

a)

b)

c)

a)

b)

c)