Droplet-scaling versus replica symmetry breaking debate in spin glasses revisited.

Abstract

Simulational studies of spin glasses since the early 2010s have focused on the so-called replicon exponent α as a means of determining whether the low-temperature phase of spin glasses is described by the replica symmetry breaking picture of Parisi or by the droplet-scaling picture. On the latter picture, it should be zero, but we shall argue that it will only be zero for systems of linear dimension L>L^{*}. The crossover length L^{*} may be of the order of hundreds of lattice spacings in three dimensions and approach infinity in six dimensions. We use the droplet-scaling picture to show that the apparent nonzero value of α when L<L^{*} should be 2θ, where θ is the domain wall energy scaling exponent. This formula is in reasonable agreement with the reported values of α.