Rg Flows in the $D$-Series of Minimal Cfts

Using results of the thermodynamic Bethe Ansatz approach and conformal perturbation theory we argue that the $\phi_{1,3}$-perturbation of a unitary minimal $(1+1)$-dimensional conformal field theory (CFT) in the $D$-series of modular invariant partition functions induces a renormalization group (RG) flow to the next-lower model in the $D$-series. An exception is the first model in the series, the 3-state Potts CFT, which under the $\ZZ_2$-even $\phi_{1,3}$-perturbation flows to the tricritical Ising CFT, the second model in the $A$-series. We present arguments that in the $A$-series flow corresponding to this exceptional case, interpolating between the tetracritical and the tricritical Ising CFT, the IR fixed point is approached from ``exactly the opposite direction''. Our results indicate how (most of) the relevant conformal fields evolve from the UV to the IR CFT.