Critical Exponents Can Be Different on the Two Sides of a Transition: A Generic Mechanism

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 Zq-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<Tc.