• Corpus ID: 16108668

The Aizenman-Sims-Starr scheme for the SK model with multidimensional spins

  title={The Aizenman-Sims-Starr scheme for the SK model with multidimensional spins},
  author={Anton Bovier and Anton Klimovsky},
  journal={arXiv: Probability},
The non-hierarchical correlation structure of the Sherrington-Kirkpatrick (SK) model with multidimensional (e.g. Heisenberg) spins is studied at the level of the logarithmic asymptotic of the corresponding sum of the correlated exponentials -- the thermodynamic pressure. For this purpose an abstract quenched large deviations principle (LDP) of Gaertner-Ellis type is obtained under an assumption of measure concentration. With the aid of this principle the framework of the Aizenman-Sims-Starr… 
1 Citations
Fluctuations of the partition function in the generalized random energy model with external field
We study Derrida’s generalized random energy model (GREM) in the presence of uniform external field. We compute the fluctuations of the ground state and of the partition function in the thermodynamic


On the overlap in the multiple spherical SK models
In order to study certain questions concerning the distribution of the overlap in Sherrington-Kirkpatrick type models, such as the chaos and ultrametricity problems, it seems natural to study the
The Sherrington-Kirkpatrick spin glass model has been studied as a source of insight into the statistical mechanics of systems with hi ghly diversified collections of competing low energy states. The
High temperature regime for a multidimensional Sherrington–Kirkpatrick model of spin glass
Abstract. Comets and Neveu have initiated in [5] a method to prove convergence of the partition function of disordered systems to a log-normal random variable in the high temperature regime by means
Extended variational principle for the Sherrington-Kirkpatrick spin-glass model
The recent proof by Guerra that the Parisi ansatz provides a lower bound on the free energy of the Sherringtun-Kirkpatrick (SK) spin-glass model could have been taken as offering some support to the
The Thermodynamic Limit in Mean Field Spin Glass Models
Abstract: We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as
An Extended Variational Principle for the SK Spin-Glass Model
The recent proof by F. Guerra that the Parisi ansatz provides a lower bound on the free energy of the SK spin-glass model could have been taken as offering some support to the validity of the
Spin glasses : a challenge for mathematicians : cavity and mean field models
0. Introduction.- 1. A Toy Model, the REM.- 2. The Sherrington-Kirkpatrick Model.- 3. The Capacity of the Perceptron: The Ising Case.- 4. Capacity of the Perceptron: The Gaussian and the Spherical
A Proof that the Free Energy of a Spin System is Extensive
The free energy obtained from the canonical partition function for a finite spin system possesses a certain convexity property, of which theorems by Peierls and Bogoliubov are particular
Some comments on the Sherrington-Kirkpatrick model of spin glasses
In this paper the high-temperature phase of general mean-field spin glass models, including the Sherrington-Kirkpatrick (SK) model, is analyzed. The free energy in zero magnetic field is calculated
Statistical Mechanics of Disordered Systems
Our mathematical understanding of the statistical mechanics of disordered systems is going through a period of stunning progress. This self-contained book is a graduate-level introduction for