  The Ising spin-glass model on the three-dimensional (d=3) hierarchical
lattice with long-range ferromagnetic or spin-glass interactions is studied by
the exact renormalization-group solution of the hierarchical lattice. The
chaotic characteristics of the spin-glass phases are extracted in the form of
our calculated, in this case continuously varying, Lyapunov exponents.
Ferromagnetic long-range interactions break the usual symmetry of the
spin-glass phase diagram. This phase-diagram symmetry-breaking is dramatic, as
it is underpinned by renormalization-group peninsular flows of the Potts
multicritical type. A Berezinski-Kosterlitz-Thouless (BKT) phase with algebraic
order and a BKT-spinglass phase transition with continuously varying critical
exponents are seen. Similarly, for spin-glass long-range interactions, the
Potts mechanism is also seen, by the mutual annihilation of stable and unstable
fixed distributions causing the abrupt change of the phase diagram. On one side
of this abrupt change, two distinct spin-glass phases, with finite (chaotic)
and infinite (chaotic) coupling asymptotic behaviors are seen with a
spin-glass-to-spin-glass phase transition.
