Fig. 2: Quasiperiodic Potts (q = 3) and Ising (q = 2) chains.

For the Ising chain we choose a potential with both positive and negative couplings, whereas for the Potts chain all couplings are taken to be antiferromagnetic. a Scaling collapse of the probability of the RG to end in a paramagnetic phase for the Potts model, with ν = 1. Here, g = W_h/W_J is an asymmetry parameter between h_i and J_i with W_J,h the amplitude of the quasiperiodic potentials and g_c = 1. Inset: Raw, uncollapsed data. b Spin–spin correlation function \(\left\langle {\sigma \left( L \right)\sigma \left( 0 \right)} \right\rangle\) averaged over the uncorrelated phases θ_J, θ_h, scaling as L^−0.47 for Potts (in good agreement with (6) derived for discrete Fibonacci sequences) and L^−0.9 for Ising. Error bars represent SE. c Energy-length scaling: ΔE ~ L^{−0.22 ln L} for Potts, whereas the Ising transition has a finite dynamical exponent z ≈ 1.6.