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I'm having trouble with this statistical physics thing again. I am given this exercise:

Problem 9 – A spin model

In a solid at temperature T the atoms have spin 1 so that the m quantum number takes on the values m = 0, ±1. Due to an interaction with the electrostatic field in the crystal, the states with m = ±1 have an energy which is higher by ε than the state with m = 0.

1.Find the average energy E(T) of the nuclei and the associated heat capacity [tex]C_V(T)[/tex]. Sketch both functions.

I'm really confused about some basic things here. The Boltzmann distribution states that:

[tex]p_r = \frac1{Z}\exp{(-E_r/kT)}.[/tex]

This is the probability that the system will be in a particular staterwith energy [tex]E_r[/tex], right? I don't know the number of states of the system or their energies - I know only the individual energies of the atoms.

I have nevertheless tried to determine the mean energy as a function of the temperature in various ways and I always end up with a function that approaches some constant value asymptotically at large temperatures. This would correspond to the heat capacity approaching zero as T tends to infinity (the heat capacity, [tex]C_V(T)[/tex], being the derivative of E(T)), which I don't think makes sense. I don't know if I'm making myself clear...

Any help would be appreciated.

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# Homework Help: Statistical physics

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