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The low-temperature Sherrington–Kirkpatrick fluctuation law
For every fixed inverse temperature β > 1, determines the fluctuation scale and limiting law of the zero-field Gaussian Sherrington–Kirkpatrick log partition function. Its variance is asymptotic to , with , confirming the predicted n standard-deviation scale. Exact centering and standardization give full-sequence convergence to a uniquely characterized nondegenerate law.
Manuscripts in this family · 2
The low-temperature Sherrington–Kirkpatrick free-energy limiting law
Sep 24, 2026·The-low-temperature-Sherrington-Kirkpatrick-free-energy-limiting-law-September-24-2026.pdf
For every fixed inverse temperature β > 1, we prove that the zero-field Gaussian Ising Sherrington–Kirkpatrick free energy, centered by its expectation and divided by its standard deviation, converges in distribution to a nondegenerate law as the system size tends to infinity through all integers. We also prove that its variance divided by n converges to a finite positive constant.
The low-temperature Sherrington–Kirkpatrick fluctuation scale
Sep 24, 2026·The-low-temperature-Sherrington-Kirkpatrick-fluctuation-scale-September-24-2026.pdf
For the zero-field Gaussian Sherrington–Kirkpatrick model at every fixed inverse temperature β > 1, we prove that the standard deviation of the log partition function is . The same exponent describes its typical centered absolute fluctuations, establishing the predicted one-sixth exponent in this regime.