Frontiers in Physics (Nov 2024)
Critical droplets and replica symmetry breaking
Abstract
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.
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