1-dimensional Ising model

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

The energy of the system will be given by

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle U=-K\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:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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.

to be continued ...