Complexity in the Sherrington-Kirkpatrick model in the annealed approximation
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 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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– 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...
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We develop a cavity method in the spherical Sherrington-Kirkpatrick model at high temperature and small external field. As an application we carry out second moment computations for the overlap and magnetization.
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ژورنال
عنوان ژورنال: Physical Review B
سال: 2003
ISSN: 0163-1829,1095-3795
DOI: 10.1103/physrevb.68.174401