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Low-temperature SK free-energy fluctuations

A limiting thermodynamic free-energy density does not describe sample-to-sample fluctuations of total free energy.

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Understanding the problem

Read the background

A limiting thermodynamic free-energy density does not describe sample-to-sample fluctuations of total free energy. The target supplies a variance scale and a normalized limiting law in the low-temperature regime.

Temperature is fixed below the transition, the field is zero, and disorder is Gaussian. This is total log-partition free energy, not the free-energy density or an assertion for every spin-glass model.

Why it matters

If correct, establishes a scoped fluctuation scale and limiting-law result beyond the limiting mean free energy.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • Temperature is fixed below the transition, the field is zero, and disorder is Gaussian. This is total log-partition free energy, not the free-energy density or an assertion for every spin-glass model.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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