1-dimensional Ising model
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