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arXiv · 2410.20610

Critical Droplets and Replica Symmetry Breaking

C. M. Newman·D. L. Stein
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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.

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C. M. Newman, D. L. Stein. 2024-11-22. Critical Droplets and Replica Symmetry Breaking. https://doi.org/10.3389/fphy.2024.1473378

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