Partition function

$Z(\beta ):=\mathrm{Tr}[e^{\beta H}]$ where

• $\beta =(k_{\beta }T{)}^{-1}$
• $T$ is the temperature
• $k_{\beta }$ is Boltzmann’s constant
• $H$ is the Hamiltonian of the system
• $\mathrm{Tr}[\cdot ]$ is the Trace operator