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I just learned some introductory quantum meachnics, but not statistical mechanics, so I am curious how partition functions would be used in the following case:

Suppose there are three particles in x-axis. These particles all have spin 1/2. Neighboring two particles interact with interaction energy of U. (particle A--particle B -- particle C, particle C and A do not (mutually) interact.)

In temperature T, what would partition function look like, what would be the meaning of this function?

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