# Quantum partition function for spins

I am trying to understand the quantum partition function for spins. The quantum partition function is

$$Z=\text{tr}\left( e^{-\beta \hat{H}} \right)$$

where tr is the trace, and $\hat{H}$ is the Hamiltonian operator for the system. How would I define a N spin system using an Hamiltonian operator and solve it in the partition function?

• In general the solvability of the partition function depends on the details of the Hamiltonian, e.g. if and how the spins are coupled. Do you have a particular Hamiltonian in mind? – Oliver Lunt Sep 3 '17 at 16:11
• @Oliver yeah, N spins that are independent of each other. A classical mixture of spins. – Alexandre H. Tremblay Sep 3 '17 at 16:36
• Are the spins in a magnetic field? – Oliver Lunt Sep 3 '17 at 20:53
• @Oliver No, just basic spins in empty space – Alexandre H. Tremblay Sep 3 '17 at 22:23