Replica symmetry breaking and exponential inequalities for the Sherrington-Kirkpatrick model
نویسندگان
چکیده
منابع مشابه
Exponential control of overlap in the replica method for p - spin Sherrington - Kirkpatrick model
In [8] the large deviations limit limN→∞(Na) −1 log EZa N for the moments of the partition function ZN in the Sherrington-Kirkpatrick model [5] was computed for all real a ≥ 0. For a ≥ 1 this result extends the classical physicist’s replica method that corresponds to integer a. We give a new proof for a ≥ 1 in the case of the pure p-spin SK model that provides a strong exponential control of th...
متن کاملThe 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...
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We investigate generalized Sherrington-Kirkpatrick glassy systems without reflection symmetry. In the neighborhood of the transition temperature, we, in general, uncover the structure of the glass state building the full-replica-symmetry-breaking solution. A physical example of the explicitly constructed solution is given.
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...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2000
ISSN: 0091-1798
DOI: 10.1214/aop/1019160325