On the Distribution of Overlaps in the Sherrington-kirkpatrick Spin Glass Model
نویسنده
چکیده
|This expository paper describes some of the analytic tools developed recently by S. Ghirlanda and F. Guerra in the investigation of the distribution of overlaps in the Sherrington-Kirkpatrick spin glass model and of Parisi's ultrametricity. In particular, we introduce to this task a simpliied model on which the Gaussian analysis is made easier, and describe, under the essential tool of self-averaging, several overlap identities. We tried to present these results in a language accessible to probabilists and analysts.
منابع مشابه
About the Overlap Distribution in Mean Field Spin Glass Modelsz
We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean eld spin glass model. Here we establish some properties of the distribution of overlaps between real replicas. They are in full agreement with the Parisi accepted picture of spontaneous replica symmetry breaking. As a byproduct, we show that the selfaveraging of the Edwards-Anderson uctuating ...
متن کاملSome Rigorous Results on the Sherrington-Kirkpatrick Spin Glass Model
We prove that in the high temperature regime (T/J > 1) the deviation of the total free energy of the Sherrington-Kirkpatrick (S-K) spin glass model from the easily computed logAv(ZN({βJ})) converges in distribution, as ΛΓ-KX), to a (shifted) Gaussian variable. Some weak results about the low temperature regime are also obtained.
متن کاملThe infinite volume limit in generalized mean field disordered models
We generalize the strategy, we recently introduced to prove the existence of the thermodynamic limit for the Sherrington-Kirkpatrick and p-spin models, to a wider class of mean field spin glass systems, including models with multi-component and non-Ising type spins, mean field spin glasses with an additional Curie-Weiss interaction, and systems consisting of several replicas of the spin glass m...
متن کاملAn exact relation between free energy fluctuations and bond chaos in the Sherrington-Kirkpatrick model
Using a variant of the interpolating Hamiltonian technique, we show that there exists, in the Sherrington-Kirkpatrick spin glass, an exact connection between the sample-to-sample fluctuations of the free energy and bond chaos involving 2and 4-replica overlaps between replicas with different but correlated bonds. This relation is used to derive an upper bound of the fluctuations. PACS numbers: 7...
متن کاملEvidence of non-mean-field-like low-temperature behavior in the Edwards-Anderson spin-glass model.
The three-dimensional Edwards-Anderson and mean-field Sherrington-Kirkpatrick Ising spin glasses are studied via large-scale Monte Carlo simulations at low temperatures, deep within the spin-glass phase. Performing a careful statistical analysis of several thousand independent disorder realizations and using an observable that detects peaks in the overlap distribution, we show that the Sherring...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007