Scaling solutions in a continuous dimension

We study scaling solutions of the RG flow equation for Z2-effective potentials in a continuous dimension d ⩾ 2. As the dimension is lowered from d = 4 we first observe the appearance of the Ising scaling solution and successively the appearance of multi-critical scaling solutions of arbitrary order. Approaching d = 2 these multi-critical scaling solutions converge to the unitary minimal models found in conformal field theory. (paper)