Ju n 20 05 Free energy in the generalized Sherrington - Kirkpatrick mean field model
نویسنده
چکیده
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.
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...
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...
متن کاملFree-Energy Barriers in the Sherrington-Kirkpatrick Model
– The Sherrington-Kirkpatrick spin-glass model is investigated by means of Monte Carlo simulations employing a combination of the multi-overlap algorithm with parallel tempering methods. We investigate the finite-size scaling behaviour of the free-energy barriers which are visible in the probability density of the Parisi overlap parameter. Assuming that the mean barrier height diverges with the...
متن کاملQuadratic replica coupling in the Sherrington-Kirkpatrick mean field spin glass model
We develop a very simple method to study the high temperature, or equivalently high external field, behavior of the Sherrington-Kirkpatrick mean field spin glass model. The basic idea is to couple two different replicas with a quadratic term, trying to push out the two replica overlap from its replica symmetric value. In the case of zero external field, our results reproduce the well known vali...
متن کامل1 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].
متن کامل