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    "title": "Ising: why a one-dimensional magnetic chain fails to retain order",
    "summary": "The1925paper calculates equilibrium magnetization for a two-orientation,nearest-neighbor linear chain by counting configurations and summing a partition function. Its large-chain result explains why this finite-interaction model lacks spontaneous magnetization at positive temperature.\n\nImagine a row of tiny magnets whose neighbors prefer to align. Alignment saves energy,but there are many ways to break the row into opposing groups. Ising made that competition calculable. His one-dimensional result survives as a useful exact model; the paper's attempt to extend the same conclusion to spatial magnets does not. Dimension,temperature and the strength of interactions matter,so a negative result in one model cannot settle a whole field.",
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        "description": "The supported target is a two-state, nearest-neighbor classical chain at positive finite temperature. Its absence of spontaneous magnetization in the stated large-chain limit does not generalize to arbitrary dimensions or interactions. Finite-chain zero-field symmetry alone is not the full thermodynamic argument. Zero temperature, long-range interactions and different spin models are outside scope. Ising’s attempted spatial extension is not adopted; Onsager’s later two-dimensional transition remains a separate contribution. WRS has not independently reconstructed all formulas or certified a physical experiment.",
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      "sources": [
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          "url": "https://www.tha.de/homes/harsch/anglica/Chronology/20thC/Ising/isi_fm00.html"
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      "statement": "# Ising: why a one-dimensional magnetic chain fails to retain order\n\nThe1925paper calculates equilibrium magnetization for a two-orientation,nearest-neighbor linear chain by counting configurations and summing a partition function. Its large-chain result explains why this finite-interaction model lacks spontaneous magnetization at positive temperature.\n\nImagine a row of tiny magnets whose neighbors prefer to align. Alignment saves energy,but there are many ways to break the row into opposing groups. Ising made that competition calculable. His one-dimensional result survives as a useful exact model; the paper's attempt to extend the same conclusion to spatial magnets does not. Dimension,temperature and the strength of interactions matter,so a negative result in one model cannot settle a whole field.\n\n## Scientific scope\n\nThe supported target is a two-state, nearest-neighbor classical chain at positive finite temperature. Its absence of spontaneous magnetization in the stated large-chain limit does not generalize to arbitrary dimensions or interactions. Finite-chain zero-field symmetry alone is not the full thermodynamic argument. Zero temperature, long-range interactions and different spin models are outside scope. Ising’s attempted spatial extension is not adopted; Onsager’s later two-dimensional transition remains a separate contribution. WRS has not independently reconstructed all formulas or certified a physical experiment.\n\n## People and systems\n\nErnst Ising\n\n\n\n## Original sources\n\n- [Ising:Contribution to the Theory of Ferromagnetism(1925), scholarly English transcription](https://www.tha.de/homes/harsch/anglica/Chronology/20thC/Ising/isi_fm00.html)\n- [Ising1924dissertation,selected original-language transcription](https://www.tha.de/homes/harsch/germanica/Chronologie/20Jh/Ising/isi_fe02.html)\n- [Springer:Ising1925originalpublicationmetadata](https://link.springer.com/article/10.1007/BF02980577)\n- [Onsager1944publisherabstract:two-dimensional order-disorder transition](https://journals.aps.org/pr/abstract/10.1103/PhysRev.65.117)\n",
      "summary": "The1925paper calculates equilibrium magnetization for a two-orientation,nearest-neighbor linear chain by counting configurations and summing a partition function. Its large-chain result explains why this finite-interaction model lacks spontaneous magnetization at positive temperature.\n\nImagine a row of tiny magnets whose neighbors prefer to align. Alignment saves energy,but there are many ways to break the row into opposing groups. Ising made that competition calculable. His one-dimensional result survives as a useful exact model; the paper's attempt to extend the same conclusion to spatial magnets does not. Dimension,temperature and the strength of interactions matter,so a negative result in one model cannot settle a whole field.",
      "title": "Ising: why a one-dimensional magnetic chain fails to retain order"
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