1-dimensional Ising model

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The 1-dimensional Ising model is an Ising model that consists of a system with spins in a row. The energy of the system is 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

References[edit]

  1. Rodney J. Baxter "Exactly Solved Models in Statistical Mechanics", Academic Press (1982) ISBN 0120831821 Chapter 2 (freely available pdf)