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:

$Q_N={\sum }_{{\mathrm{\Omega }}^N}\exp [K\sum _{i=1}^{N-1}{S}_i{S}_{i+1}]$,

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

to be continued ...