The influence of critical behavior on the spin glass phase

Abstract

We have argued in recent papers that Monte Carlo results for the equilibrium properties of the Edwards-Anderson spin glass in three dimensions, which had been interpreted earlier as providing evidence for replica symmetry breaking, can be explained quite simply within the droplet model once finite size effects and proximity to the critical point are taken into account. In this paper, we show that similar considerations are sufficient to explain the Monte Carlo data in four dimensions. In particular, we study the Parisi overlap and the link overlap for the four-dimensional Ising spin glass in the Migdal-Kadanoff approximation. Similar to what is seen in three dimensions, we find that temperatures well below those studied in Monte Carlo simulations have to be reached before the droplet model predictions become apparent. We also show that the double-peak structure of the link overlap distribution function is related to the difference between domain-wall excitations that cross the entire system and droplet excitations that are confined to a smaller region.

8 pages, 8 figures

References in corpus (6)

• Triviality of the Ground State Structure in Ising Spin Glasses
• Calculation of ground states of four-dimensional +or- J Ising spin glasses
• The Link Overlap and Finite Size Effects for the 3D Ising Spin Glass
• Comment on "General Method to Determine Replica Symmetry Breaking Transitions"
• Scaling and infrared divergences in the replica field theory of the Ising spin glass
• Reply to "Comment on Evidence for the droplet picture of spin glasses"

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