PhysicsLogic / Mermin-Wagner 1966

What an Ordered Limit Requires

Inspect spin observables, finite Gibbs coordinates, and the quantifiers behind infinite volume and vanishing field.

Definitions and assumptions

Scope and physical limitations

The two-orientation example is a diagnostic, not a short-range Heisenberg model or a counterexample to Mermin-Wagner. The epsilon/delta equivalences characterize the library's iterated limits, not a joint limit or uniform convergence.

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Examples and distinctions

Constructed examples of this model; each answer includes the Lean statement.

Exact root statement

MagneticLimitControls.twoPhaseFamily.HasFirstThenSecondLimitAt 1 ∧
  MagneticLimitControls.twoPhaseFamily.swap.HasFirstThenSecondLimitAt 0 ∧
    MagneticLimitControls.twoPhaseFamily.NoncommutingLimitsAt
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Notes and questions

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Definitions, structures, and assumptions

Structures, classes, and inductive alternatives

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Definitions and domain choices

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Checked statements: parameters, hypotheses, and interpretation

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Constructors, projections, and other meaning dependencies

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External mathematical declarations

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