  This paper is divided into two parts. The first part concerns several
standard scenarios for how short-range spin glasses might behave at low
temperature. Earlier theorems of the authors are reviewed, and some new results
presented, including a proof that, in a thermodynamic system exhibiting
infinitely many pure states and with the property (such as in
replica-symmetry-breaking scenarios) that mixtures of these states manifest
themselves in large finite volumes, there must be an uncountable infinity of
states. In the second part of the paper, we offer some conjectures and
speculations on possible unusual scenarios for the low-temperature phase of
finite-range spin glasses in various dimensions. We include a discussion of the
possibility of a phase transition without broken spin-flip symmetry, and
provide an argument suggesting that in low dimensions such a possibility may
occur. The argument is based on a new proof of Fortuin-Kasteleyn random cluster
percolation at nonzero temperatures in dimensions as low as two. A second
speculation considers the possibility, in analogy to certain phenomena in
Anderson localization theory, of a much stronger type of chaotic temperature
dependence than has previously been discussed: one in which the actual state
space structure, and not just the correlations, vary chaotically with
temperature.
