{
  "annotation_id": "f4d75d78-324e-479d-bc1f-4798bff62b48",
  "date_created": "2026-03-02T18:02:16.541000Z",
  "date_modified": "2026-03-02T18:02:16.541000Z",
  "file_hash": "0e89741dfd41c44cd33df64b8492300c66c09cb3f9f5926ae1291cee0e24b373",
  "private": false,
  "record": {
    "abstract": "The periodic boundary conditions changed the plane square-lattice Ising model\nto the torus-lattice system which restricts the spin-projection orientations.\nOnly two of the three important spin-projection orientations, parallel to the\nx-axis or to the y-axis, are suited to the torus-lattice system. The\ninfinitesimal difference of the free-energies of the systems between the two\nsystems mentioned above makes their critical temperatures infinitely close to\neach other, but their topological fundamental groups are distinct.",
    "arxiv_id": "quant-ph/0506202",
    "authors": [
      "You-gang Feng"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Spin-projection orientations in the plane square-lattice Ising model   with periodic boundary conditions",
    "url": "https://arxiv.org/abs/quant-ph/0506202"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ad0a26f1-da2d-409e-83d8-c90cb3afaba6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}