{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"78125e5c9817ac6445f046a4f93f4f6a8c36685a67d6380a95c08b7839b9ecfc","created":"2026-10-03T07:18:01Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"a51187fe1ce21c7e082b1f1adf138e68c431f8282fa12f7ef6739e0956ebdf42","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.quantum-spin-glasses.heisenberg-glass-ground-state","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"When quantum spins free to point in any direction interact with random couplings of both signs, they may freeze into a glass or stay in a liquid-like state with no frozen moments. For spin $1/2$ with all-to-all random couplings, calculations suggest weak freezing, but its size and the liquid-like behavior above it are unsettled, and short-range versions are open.","posed_since":"1993","precise":"Model: $H = (1/\\sqrt{N}) \\sum_{i<j} J_{ij} S_i . S_j$, $S = 1/2$, $J_{ij}$ independent Gaussian with zero mean and unit variance, and its short-range versions on 2D and 3D lattices. Determine whether the Edwards-Anderson order parameter $q_{\\mathrm{EA}}$, the long-time limit of the site- and disorder-averaged $\\langle S_i(t) . S_i(0)\\rangle$, is nonzero at $T = 0$ in the thermodynamic limit, its value, and the temperature window in which Sachdev-Ye spin-liquid correlations $G(\\tau)\\sim 1/\\tau$ appear. An answer gives $q_{\\mathrm{EA}}$ with error bars and the crossover temperature.","problem_ref":null,"references":"","settled_by":"Extrapolation in N of exact-diagonalization and matrix-product-state data for the infinite-range model, checked against controlled large-M expansions of its SU(M) generalization, and quantum Monte Carlo or tensor-network data for the lattice versions.","status_note":"Christos, Haehl and Sachdev (PRB 2022) described spin-glass order at $T = 0$ with a spin-liquid crossover at higher $T$, and Hosseinabadi, Sachdev and Marino (PRL 2026) studied the crossover to Sachdev-Ye-Kitaev criticality; the short-range lattice versions are open.","title":"Does the random SU(2) Heisenberg magnet freeze at zero 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