{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"3d92df7e6802b7e288fc5a395606479214ee451669b3a5da213bccdf77d63092","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"caf212d5d4d65fb014a40687c22934692124d0dca979567cf2710c10f92cb9ea","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"stat.spin-glass-finite-d.low-temperature-phase","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Below its freezing temperature, does a three-dimensional spin glass have many distinct frozen states, as in the solvable infinite-range model, or essentially one state and its mirror image? The two pictures predict different responses to small changes in temperature or magnetic field.","posed_since":"1986","precise":"For the 3D Edwards-Anderson Ising model H = -sum_<ij> J_ij s_i s_j with symmetric Gaussian or $\\pm J$ couplings at $T < T_c$, determine in the thermodynamic limit whether the spin overlap distribution $P(q)$ keeps a continuous part between $-q_{\\mathrm{EA}}$ and $q_{\\mathrm{EA}}$ (replica symmetry breaking, RSB), whether system-spanning excitations cost $O(1)$ energy (RSB) or grow as $L^{\\theta}$ with $\\theta > 0$ (droplet picture), or whether the intermediate trivial-nontrivial (TNT) scenario holds. An answer is one of these classifications supported by finite-size analysis that controls the $L \\to \\infty$ limit, or by a proof.","problem_ref":null,"references":"","settled_by":"Equilibrium simulations or ground-state computations at sizes large enough to fix the L dependence of P(q) and of domain-wall and sponge excitation energies without ambiguity.","status_note":"Simulations at accessible sizes look RSB-like, while droplet proponents argue these sizes are preasymptotic (M. A. Moore, arXiv:2103.02973, 2021).","title":"Replica symmetry breaking or droplets in the 3D Edwards-Anderson 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