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 dimension. Given a specific ground state, suppose 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.

12 pages, no figures, new version includes a Note Added in Proof and an additional reference ([38]). arXiv admin note: text overlap with arXiv:2110.11229

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Cited by in corpus (1)

• SpinGlassPEPS.jl: Tensor-network package for Ising-like optimization on quasi-two-dimensional graphs