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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?

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  • $\begingroup$ 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? $\endgroup$ – Oliver Lunt Sep 3 '17 at 16:11
  • $\begingroup$ @Oliver yeah, N spins that are independent of each other. A classical mixture of spins. $\endgroup$ – Alexandre H. Tremblay Sep 3 '17 at 16:36
  • $\begingroup$ Are the spins in a magnetic field? $\endgroup$ – Oliver Lunt Sep 3 '17 at 20:53
  • $\begingroup$ @Oliver No, just basic spins in empty space $\endgroup$ – Alexandre H. Tremblay Sep 3 '17 at 22:23

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