Many systems near criticality can be described by Hamiltonians involving several relevant couplings and possessing many nontrivial fixed points. A simple and physically appealing characterization of the crossover lines and surfaces connecting different nontrivial fixed points is presented. Generalized crossover is related to the vanishing of the renormalization group function Z(-1)(t). An explicit example is discussed in detail based on the tetragonal Landau-Ginzburg-Wilson Hamiltonian.
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