On the High Temperature Phase of the Sherrington-Kirkpatrick Model
نویسندگان
چکیده
منابع مشابه
The Sherrington-Kirkpatrick model
The Sherrington-Kirkpatrick (SK) model was introduced by David Sherrington and Scott Kirkpatrick in 1975 as a simple ‘solvable’ (in their words) model for spin-glasses. Spin-glasses are some type of magnetic alloys, and ‘solvable’ meant that the asymptotic free entropy density could be computed exactly. It turns out that the original SK solution was incorrect and in fact inconsistent (the autho...
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The state of art in spin glass field theory is reviewed. We start from an Edwards-Anderson-type model in finite dimensions, with finite but long range forces, construct the effective field theory that allows one to extract the long wavelength behaviour of the model, and set up an expansion scheme (the loop expansion) in the inverse range of the interaction. At the zeroth order we recover mean f...
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In this paper we explore the joint behaviour of a finite number of multioverlaps in the high temperature phase of the SK model. Extending work by M. Talagrand, we show that, when these objects are scaled to have non-trivial limiting distributions, the joint behaviour is described by a Gaussian process with an explicit covariance structure.
متن کاملOn the energy minima of the Sherrington–Kirkpatrick model
We study properties of the energy minima obtained by quenching equilibrium configurations of the Sherrington–Kirkpatrick (SK) mean-field spin glass. We measure the probability distribution of the overlap among quenched configurations and the quenched energy, looking at the dependence on the starting equilibrium temperature, and performing a systematic analysis of finite-size effects.
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In a region above the Almeida-Thouless line, where we are able to control the thermodynamic limit of the Sherrington-Kirkpatrick model and to prove replica symmetry, we show that the fluctuations of the overlaps and of the free energy are Gaussian, on the scale 1/ √ N , for N large. The method we employ is based on the idea, we recently developed, of introducing quadratic coupling between two r...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2002
ISSN: 0091-1798
DOI: 10.1214/aop/1020107771