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A typical example is the class of the Ising model; adding a next-nearest-neighbour hopping term does not change the critical behavior. The typical explanation is that the 'physics on scales much longer than the lattice spacing does not depend on these interactions'.

My question is: are there any rules of thumb that determine how far a model must be changed before it changes the universality class? And when it does so, will there be a continuous crossover?

A possibility would probably be adding some different arbitrary-range coupling terms in the Hamiltonian. But on the other hand, the Ising model as I described does not contain any explicit long-range terms, although this does not say that every local model is in the quantum-ising universality class...

Note: I know my question is also valid with classical PT, but I'm posting it in this subforum since the QPT is of most interest to me at the moment.