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We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards–Anderson–Ising model of a spin glass in arbitrary dimensions. Given a specific ground state, we suppose that the coupling value for a given edge is varied with all other couplings held fixed. Beyond some specific value of the coupling, a droplet will flip, leading to a new ground state; we refer to this as the critical droplet for that edge and ground state. We show that the distribution of sizes and energies over all edges for a specific ground state can be used to determine which of the leading scenarios for the spin glass phase is correct. In particular, the existence of low-energy interfaces between incongruent ground states, as predicted by replica symmetry breaking, is equivalent to the presence of critical droplets, whose boundaries comprise a positive fraction of edges in the infinite lattice. [ABSTRACT FROM AUTHOR]

We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards–Anderson–Ising model of a spin glass in arbitrary dimensions. Given a specific ground state, we suppose that the coupling value for a given edge is varied with all other couplings held fixed. Beyond some specific value of the coupling, a droplet will flip, leading to a new ground state; we refer to this as the critical droplet for that edge and ground state. We show that the distribution of sizes and energies over all edges for a specific ground state can be used to determine which of the leading scenarios for the spin glass phase is correct. In particular, the existence of low-energy interfaces between incongruent ground states, as predicted by replica symmetry breaking, is equivalent to the presence of critical droplets, whose boundaries comprise a positive fraction of edges in the infinite lattice.