1 8 M ay 2 00 4 Free energy in the generalized Sherrington - Kirkpatrick mean field model . Dmitry Panchenko
نویسنده
چکیده
In [11] Michel Talagrand gave a rigorous proof of the Parisi formula in the SherringtonKirkpatrick model. In this paper we build upon the methodology developed in [11] and extend Talagrand’s result to a more general class of mean field models with spins distributed according to an arbitrary probability measure on the bounded subset of the real line and with external field term given by an arbitrary bounded function of the spin.
منابع مشابه
1 8 M ay 2 00 4 Free energy in the Sherrington - Kirkpatrick model with the constraint on the average of spins
In his recent paper [6] Michel Talagrand gave a rigorous proof of the Parisi formula for the free energy of the Sherrington-Kirkpatrick model. In the present paper we utilize the methodology developed in [6] to compute the thermodynamic limit of the free energy of the set of configurations with the fixed average of spins N−1 ∑ i≤N σi = uN as uN → u ∈ [−1, 1].
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In this paper we consider a system of spins that consists of two configurations σ 1,σ2 ∈ ΣN = {−1,+1}N with Gaussian Hamiltonians H1 N (σ1) and H2 N (σ2) correspondingly, and these configurations are coupled on the set where their overlap is fixed {R1,2 = N−1 ∑N i=1 σ 1 i σ 2 i = uN}. We prove the existence of the thermodynamic limit of the free energy of this system given that limN→∞ uN = u ∈ ...
متن کاملJu n 20 05 Free energy in the generalized Sherrington - Kirkpatrick mean field model
In [11] Michel Talagrand gave a rigorous proof of the Parisi formula in the classical Sherrington-Kirkpatrick (SK) model. In this paper we build upon the methodology developed in [11] and extend Talagrand’s result to the class of SK type models in which the spins have arbitrary prior distribution on a bounded subset of the real line.
متن کاملM ay 2 00 4 A central limit theorem for weighted averages of spins in the high temperature region of the Sherrington - Kirkpatrick model
In this paper we prove that in the high temperature region of the SherringtonKirkpatrick model for a typical realization of the disorder the weighted average of spins ∑ i≤N tiσi will be approximately Gaussian provided that maxi≤N |ti|/ ∑ i≤N t 2 i is small.
متن کاملFree energy in the generalized Sherrington-Kirkpatrick mean field model
In [10] Michel Talagrand gave a rigorous proof of the Parisi formula in the SherringtonKirkpatrick model. In this paper we build upon the methodology developed in [10] and extend Talagrand’s result to a more general class of mean field models with spins distributed according to an arbitrary probability measure on the bounded subset of the real line and with external field term given by an arbit...
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تاریخ انتشار 2005