Influence of critical behavior on the spin-glass phase

We have argued in recent papers that the Monte Carlo results for the equili brium properties of the Edwards-Anderson spin glass in three dimensions, wh ich had been interpreted earlier as providing evidence for replica symmetry breaking, can be explained quite simply within the droplet model once fini te-size effects and proximity to the critical point are taken into account. In this paper we show that similar considerations are sufficient to explai n the Monte Carlo data in four dimensions. In particular, we study the Pari si overlap and the link overlap for the four-dimensional Ising spin glass i n the Migdal-Kadanoff approximation. Similar to what is seen in three dimen sions, we find that temperatures well below those studied in the Monte Carl o simulations have to be reached before the droplet model predictions becom e apparent. We also show that the double-peak structure of the link overlap distribution function is related to the difference between domain-wall exc itations that cross the entire system and droplet excitations that are conf ined to a smaller region.