The Parisi formula
نویسندگان
چکیده
منابع مشابه
On Differentiability of the Parisi Formula
It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate solutions in the Parisi formula and give one example of application of differentiability to prove non self-averaging of the overlap outside of the...
متن کاملThe Aizenman-Sims-Starr scheme and Parisi formula for mixed p-spin spherical models
The Parisi formula for the free energy in the spherical models with mixed even p-spin interactions was proven in Michel Talagrand [16]. In this paper we study the general mixed p-spin spherical models including p-spin interactions for odd p. We establish the Aizenman-Sims-Starr scheme and from this together with many well-known results and Dmitry Panchenko’s recent proof on the Parisi ultrametr...
متن کاملThe Untruncated Marinari-parisi Superstring
It is shown that the bosonic angular degrees of freedom in the one dimensional Marinari-Parisi superstring can be integrated out exactly in the Hamiltonian formulation without having to perform the Dabholkar truncation. The resulting Hamiltonian is that of a supersymmetric Calogero system plus a four fermions interaction. This extra interaction vanishes for all physical states with fermion numb...
متن کاملParisi Phase in a Neuron
Pattern storage by a single neuron is revisited. Generalizing Parisi's framework for spin glasses we obtain a variational free energy functional for the neuron. The solution is demonstrated at high temperature and large relative number of examples , where several phases are identified by thermodynam-ical stability analysis, two of them exhibiting spontaneous full replica symmetry breaking. We g...
متن کاملA Question about Parisi Functional
We conjecture that the Parisi functional in the Sherrington-Kirkpatrick model is convex in the functional order parameter. We prove a partial result that shows the convexity along “one-sided” directions. An interesting consequence of this result is the log-convexity of Lm norm for a class of random variables.
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2006
ISSN: 0003-486X
DOI: 10.4007/annals.2006.163.221