Hierarchical solutions of the Sherrington-Kirkpatrick model: Exact asymptotic behavior near the critical temperature
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...
متن کاملBeyond the Sherrington-kirkpatrick Model
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...
متن کاملSherrington-Kirkpatrick spin glass model
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...
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.
متن کاملThe out of equilibrium dynamics of the Sherrington-Kirkpatrick model
The analytic solution to the dynamics of the Sherrington-Kirkpatrick model was developed in the nineties. It involves directly measurable out of equilibrium quantities, and thus addresses the questions relevant to an experimental system. We here review the out of equilibrium relaxation of this model and how it compares to experimental measurements. Out of equilibrium dynamics 2
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ژورنال
عنوان ژورنال: Physical Review B
سال: 2006
ISSN: 1098-0121,1550-235X
DOI: 10.1103/physrevb.74.054410