The droplet-scaling versus replica symmetry breaking debate in spin glasses revisited

摘要: Simulational studies of spin glasses in the last decade have focussed on so-called replicon exponent $\alpha$ as a means determining whether low-temperature phase is described by replica symmetry breaking picture Parisi or droplet-scaling picture. On latter picture, it should be zero, but we shall argue that will only zero for systems linear dimension $L > L^*$. The crossover length $L^*$ may order hundreds lattice spacings three dimensions and approach infinity 6 dimensions. We use to show apparent non-zero value when < L^*$ $2 \theta$, where $\theta$ domain wall energy scaling exponent, This formula reasonable agreement with reported values $\alpha$.