We present models where γ(+) and γ(-), the exponents of the susceptibility in the high- and low-temperature phases, are generically different. In these models, continuous symmetries are explicitly broken down by discrete anisotropies that are irrelevant in the renormalization-group sense. The Z(q)-invariant models are the simplest examples for two-component order parameters (N=2) and the model with icosahedral symmetry for N=3. We accurately compute γ(+)-γ(-) as well as the ratio ν/ν' of the exponents of the two correlation lengths present for T