Competing and aperiodic interactions in the Ising chain

We investigate the effects of the inclusion of aperiodic interactions in the Ising chain with competing ferro and antiferromagnetic couplings between nearest and next-nearest-neighbor sites. In particular, we obtain the exact ground state, including the spin arrangements and the residual entropies, for an Ising chain with extra aperiodic interactions associated with the fractal rules defined by a Koch curve.