The mean field approximation : Introductory video
Before watching the video read the questions below. As you watch the video try to answer them
Questions
- Explain how the Hamiltonian for the Ising model can be approximated using the mean field approximation.
- Explain why approximating the Ising model Hamiltonian in this way simplifies the calculation of the partition function
- Write out an expression for the partition function of the Ising model when it is calculated using the mean field approximation.
- Explain how one can calculate the average spin term $\langle S \rangle$ that appears in the expression for the partition function that you have just written out by taking suitable derivatives of the partition function
- Write out an expression for the average spin that involves the $\tanh$ function
- Explain how the Hamiltonian for the Ising model can be approximated using the mean field approximation.
- Explain why approximating the Ising model Hamiltonian in this way simplifies the calculation of the partition function
- Write out an expression for the partition function of the Ising model when it is calculated using the mean field approximation.
- Explain how one can calculate the average spin term $\langle S \rangle$ that appears in the expression for the partition function that you have just written out by taking suitable derivatives of the partition function
- Write out an expression for the average spin that involves the $\tanh$ function