1 8 M ay 2 00 4 Free energy in the Sherrington - Kirkpatrick model with the constraint on the average of spins
نویسنده
چکیده
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].
منابع مشابه
1 8 M ay 2 00 4 Free energy in the generalized Sherrington - Kirkpatrick mean field model . Dmitry Panchenko
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 arbit...
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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 ∈ ...
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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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