THE ISING MODEL IN LIGHT OF THE UNIVERSALITY OF SPIN MODELS AND TURING MACHINES

Gemma De les Coves (Personal webpage)

I will explain that Ising models are universal for all other spin models in a way that is similar to universal Turing machines. In order to compare the two universalities rigorously, I will show how one can cast Ising models as formal languages and classify them in Chomsky hierarchy; in this sense, Ising models in different dimensions have regular, context free or context sensitive grammars. Finally I will show that their universality can be examined in the broader light of abstract properties of universality.