Large Deviations in Physics by Angelo Vulpiani Fabio Cecconi Massimo Cencini Andrea Puglisi & Davide Vergni

Author:Angelo Vulpiani, Fabio Cecconi, Massimo Cencini, Andrea Puglisi & Davide Vergni
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

(5.75)

or it can be computed in the original SK model,1 where also the non variational part of the free energy is included and τ is defined as [35]

(5.76)

For n > n s (τ) the replica symmetric solution remains stable.

From this result, it follows that the first non-vanishing term in the expansion of W(n) − fn is proportional to n 6, and so, from the above general result, cf. Eq. (5.67), we conclude that [25]

(5.77)

Using scaling argument one may also infer that C 2 ∼ N 1∕3.

The above prediction has been tested in recent years in numerical simulations also significantly below T c and, in particular, at T = 0 [26–33]. Kondor’s computation has been extended down to zero temperature and for higher orders in n [34, 35], generalizing Eq. (5.74) to the following expression valid at any temperature:

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