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Ising: why a one-dimensional magnetic chain fails to retain order

Contribution grade

Statistical mechanics · Statistical mechanics

Reference score210,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Configuration counting and generating-function summation calculate the nearest-neighbor two-state chain's equilibrium response; the source negative result is isolated from its incorrect spatial extrapolation.

Scientific scope

Configuration counting and generating-function summation calculate the nearest-neighbor two-state chain's equilibrium response; the source negative result is isolated from its incorrect spatial extrapolation. 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.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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