# Final remark on equivalence in statistical mechanics

The analysis that we have just carried out has shown an *equivalence* between physical models. In statistical mechanics, the term *equivalence* can be used with two different "nuances":

**exact equivalence**: this means that there is an exact mapping between the partition functions of two different models

**approximate equivalence**: this means that the partition functions of two models are*not*related by an exact mapping, but nevertheless they behave in exactly the same way near a critical point. Such models are said to belong to the same*universality class*.

Apart from the equivalence between the Ising model and neural networks, all the correspondences we have shown are exact.