The droplet picture

Throughout this book we have developed a spin glass field theory for the fluctuation field around the mean field RSB Parisi solution. The justification for such a theory, as we have stated at the beginning of our discussion, is intimately related to the validity in finite dimension of the nontrivial multi-ergodic physical scenario depicted by the mean field solution. Whether this is the case or not is still not clear. We have commented in the chapters previous to this conclusion what are the main features of the spin glass field theory, the consistency it exhibits, some reasonable extrapolations to dimensions lower than six and some possible predictions for measurable observables. Despite the great effort and the rich results obtained so far, the validity of the theory in three dimensions is still, however, a debated point, as much as the assumption of a nontrivial spin glass state at low temperature. It therefore seems important to us to briefly mention a few alternative points of view where the low temperature phase has different features from the ones we have extensively described.

The droplet model

The richest and most interesting alternative picture for the EA model was developed along the years by various authors (Bray and Moore, 1984, 1986; McMillan, 1984; Fisher and Huse, 1986, 1987, 1988; Newman and Stein, 1992, 1996, 1998) and is generally referred to as the ‘droplet model’, from the Fisher and Huse paper of 1986. The physical scenario described by this model is in striking contrast to the mean field one.