  In this paper we consider one-dimensional classical and quantum spin-1=2
quasiperiodic Ising chains, with two-valued nearest neighbor interaction
modulated by a Fibonacci substitution sequence on two letters. In the quantum
case, we investigate the energy spectrum of the Ising Hamiltonian, in presence
of constant transverse magnetic field, by employing the techniques that were
developed in our previous work. In the classical case, we investigate and prove
analyticity of the free energy function when the magnetic field, together with
interaction strength couplings, is modulated by the same Fibonacci substitution
(thus proving absence of phase transitions of any order at finite temperature).
We also investigate the distribution of Lee-Yang zeros of the partition
function in the complex magnetic field regime, and prove its Cantor set
structure (together with some additional qualitative properties), thus
providing a rigorous justification for the observations in some previous works.
In both, quantum and classical models, we concentrate on the ferromagnetic
class.
