- #1

George444fg

- 26

- 4

- TL;DR Summary
- Partition function of crystal unit cell

https://physics.stackexchange.com/users/316839/georgios-demeteiou

I have a cubic lattice, and I am trying to find the partition function and the expected value of the dipole moment. I represent the dipole moment as a unit vector pointing to one the 8 corners of the system. I know nothing about the average dipole moment , but I do know that the mean-field Hamiltonian is given by:

pi⋅⟨p⟩i⋅⟨p⟩ =H(p).

If the dipole, was oriented along all possible directions of the cubic lattice, then I would have performed an integration over spherical coordinates obtaining the usual Langevin function. Now in this scenario, I am a bit hesitant because I know nothing about the direction of the average dipole moment. Shall I assume a haphazard direction and then proceed algebraically for the summation over the 8 possible directions?

Thank you in advance

I have a cubic lattice, and I am trying to find the partition function and the expected value of the dipole moment. I represent the dipole moment as a unit vector pointing to one the 8 corners of the system. I know nothing about the average dipole moment , but I do know that the mean-field Hamiltonian is given by:

pi⋅⟨p⟩i⋅⟨p⟩ =H(p).

If the dipole, was oriented along all possible directions of the cubic lattice, then I would have performed an integration over spherical coordinates obtaining the usual Langevin function. Now in this scenario, I am a bit hesitant because I know nothing about the direction of the average dipole moment. Shall I assume a haphazard direction and then proceed algebraically for the summation over the 8 possible directions?

Thank you in advance