As a homework exercise for Advanced Statistical Mechanics I need to derive the canonical partition functions for the following systems:
- Single component ideal gas on a square lattice
- Single component ideal gas in real space
- Partition function for a lattice gas on a square lattice where each lattice site can only have a single particle, but neighbouring particles do not interact
I do not want any final answers as I would like to derive them myself, but I'd like to know a strategy on how to solve this problem. My guess is that I have to use the general formula for the canonical partition function $$ Z(N,V,T) = \sum_mexp(-\beta \epsilon_m) $$ Where $e_m$ is the energy of state $m$ and $\beta = 1/k_bT$.
Normally when solving these kind of problems I simply determine $e_m$ but I'm not sure how to do this for this problem.