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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle K = J/k_B T }

to be continued ...