Critical Exponents for Quantum Phase Transitions

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Hi All, I'm doing an undergraduate project regarding QPTs for some variation of a AF Heisenberg hamiltonian. I'm a little confused about the change in relations between the critical exponents for a QPT. Some books/papers state that the quantum system in D dimensions is mapped to a classical D + 1 dimension system at T = 0. Yet they also say that in the finite-size scaling laws, we have to change D to D + z, where z is the dynamic critical exponent. So does that mean that the universality class of the QPT is in Some D + z classical system, but beyond the critical parameter, it appears like some D + 1 classical system? Is there some kind of contradiction between these two statements, or am I missing something? I'm afraid I'm not entirely familiar with the subject so I kind of assume universality class and mapping to a new classical system are kind of the same thing. Would appreciate any help with thanks :)
 

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