Free energy fluctuations and chaos in the Sherrington-Kirkpatrick model
T. Aspelmeier
TL;DR
This paper rigorously links free energy fluctuations in the Sherrington-Kirkpatrick model to bond chaos, providing an analytical approach via replica methods and establishing an upper bound on fluctuation growth exponent.
Contribution
It introduces a rigorous connection between free energy fluctuations and bond chaos, enabling analytical calculation and bounding the fluctuation exponent.
Findings
Fluctuations are related to bond chaos.
The fluctuation growth exponent mu <= 1/4.
Analytical access via replica methods.
Abstract
The sample-to-sample fluctuations Delta F_N of the free energy in the Sherrington-Kirkpatrick model are shown rigorously to be related to bond chaos. Via this connection, the fluctuations become analytically accessible by replica methods. The replica calculation for bond chaos shows that the exponent mu governing the growth of the fluctuations with system size N, i.e. Delta F_N N^mu, is bounded by mu <= 1/4.
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