1-dimensional Ising model

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Model: Consider a system with spins in a row.

The energy of the system will be given by

,

where each variable can be either -1 or +1.

The partition function of the system will be:

,


where represents the possible configuration of the N spins of the system, and

Performing the sum of the possible values of we get:

Taking into account that

Therefore:

The Helmholtz energy function in the thermodynamic limit will be