Central Limit Theorems for the Energy Density in the Sherrington-Kirkpatrick Model
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چکیده
منابع مشابه
Central Limit Theorems for the Energy Density in the Sherrington-kirkpatrick Model
In this paper we consider central limit theorems for various macroscopic observables in the high temperature region of the Sherrington-Kirkpatrick spin glass model. With a particular focus on obtaining a quenched central limit theorem for the energy density of the system with non-zero external field, we show how to combine the mean field cavity method with Stein’s method in the quenched regime....
متن کاملCentral limit theorems for cavity and local fields of the Sherrington-Kirkpatrick model
One of the remarkable applications of the cavity method in the mean field spin glasses is to prove the validity of the Thouless-Anderson-Palmer (TAP) system of equations in the Sherrington-Kirkpatrick (SK) model in the high temperature regime. This naturally leads us to the study of the limit laws for cavity and local fields. The first quantitative results for both fields were obtained by Chatt...
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...
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...
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2009
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-009-9865-3