Free-energy fluctuations and chaos in the Sherrington-Kirkpatrick model

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, Delta F(N) similar to N(mu), is bounded by mu <= 1/4.