Quantum statistical mechanics: A many-spin system (This is a more difficult version of the previous problem)
Consider a macroscopic crystal with a spin-one quantum mechanical magnetic moment located on each of N atoms. Assume that we can represent the energy eigenvalues of the system with a Hamiltonian of the form
![1576_dee61882-bdbc-49c8-8497-d96e77907fcf.png](https://secure.tutorsglobe.com/CMSImages/1576_dee61882-bdbc-49c8-8497-d96e77907fcf.png)
where each σn takes on the values -1, 0, or +1, and B and D are constants representing an external magnetic field and a "crystal field," respectively. The entire system is in contact with a thermal reservoir at temperature T.
1. Calculate the partition function for this system.
2. Calculate the free energy of this system.
3. Calculate the magnetization per spin
![1090_5b7cd21e-45ec-49c4-a6ce-a5cdb2488249.png](https://secure.tutorsglobe.com/CMSImages/1090_5b7cd21e-45ec-49c4-a6ce-a5cdb2488249.png)
4. Calculate the entropy per spin of this system.
5. Determine whether this system satisfies the Nernst Postulate for all values of the parameters.