Large Deviation Property of Free Energy in p-Body Sherrington-Kirkpatrick Model

Details Large Deviation Property of Free Energy in p-Body Sherrington-Kirkpatrick Model Large Deviation Property of Free Energy in p-Body Sherrington-Kirkpatrick Model

2008-02-10

arxiv.org/abs/0802.1302v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 5 figures. accepted for publication in J.Phs.Soc.Jpn

Scientific paper

10.1143/JPSJ.77.074718

Cumulant generating function phi(n) and rate function Sigma(f) of the free energy is evaluated in p-body Sherrington-Kirkpatrick model by using the replica method with the replica number n finite. From a perturbational argument, we show that the cumulant generating function is constant in the vicinity of n = 0. On the other hand, with the help of two analytic properties of phi(n), the behavior of phi(n) is derived again. However this is also shown to be broken at a finite value of n, which gives a characteristic value in the rate function near the thermodynamic value of the free energy. Through the continuation of phi(n) as a function of n, we find out a way to derive the 1RSB solution at least in this model, which is to fix the RS solution to be a monotone increasing function.

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