1-dimensional Ising model

Model: Consider a system with $N$ spins in a row.

The energy of the system will be given by

$U=-J\sum _{i=1}^{N-1}S_{i}S_{i+1}$,

where each variable $S_{j}$ can be either -1 or +1.

The partition function of the system will be:

$Q_{N}=\sum _{\Omega ^{N}}\exp \left[K\sum _{i=1}^{N-1}S_{i}S_{i+1}\right]$,

where $\Omega ^{N}$ represents the possible configuration of the N spins of the system, and $K=J/k_{B}T$

to be continued ...