1-dimensional Ising model

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

The energy of the system will be given by

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 U = -K \sum_{i=1}^{N-1} S_{i} S_{i+1} } ,

where each variable 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 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 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 \Omega^N } represents the possible configuration of the N spins of the system.

to be continued ...