Free Energy Fluctuations in Ising Spin Glasses

The sample-to-sample fluctuations of the free energy in finite-dimensional Ising spin glasses are calculated, using the replica method, from higher order terms in the replica number $n$. It is shown that the Parisi symmetry breaking scheme does not give the correct answers for these higher order terms. A modified symmetry breaking scheme with the same stability is shown to resolve the problem.

Figure 1

The $q$ functions for $n^{+}$ and $n^{-}$ and the modified one for $n^{+}$ (see end of article). The three curves have been slightly shifted against each other for better visibility.