# Some comments on the Sherrington-Kirkpatrick model of spin glasses

@article{Frhlich1987SomeCO, title={Some comments on the Sherrington-Kirkpatrick model of spin glasses}, author={J{\"u}rg Fr{\"o}hlich and Boguslav Zegarlinski}, journal={Communications in Mathematical Physics}, year={1987}, volume={112}, pages={553-566} }

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 explicitly for the SK model, and uniform bounds on quenched susceptibilities are established. It is also shown that, at high temperatures, mean-field spin glasses are limits of short-range spin glasses, as the range of the interactions tends to infinity.

## 53 Citations

### Some comments on the connection between disordered long range spin glass models and their mean field version

- Mathematics
- 2003

In this paper, we consider a particular aspect of the relationship between mean field and finite-dimensional spin glasses. By means of a simple interpolation method, we prove that the free energy of…

### Nonrealistic behavior of mean-field spin glasses.

- PhysicsPhysical review letters
- 2003

Its occurrence in the SK model means that the commonly used "modified clustering" notion of states sheds little light on the replica symmetry breaking (RSB) solution of SK, and, conversely, the RSB solution sheds littleLight on the thermodynamic structure of Edwards-Anderson models.

### Central limit theorem for fluctuations in the high temperature region of the Sherrington-Kirkpatrick spin glass model

- Mathematics
- 2002

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…

### Fluctuations and thermodynamic variables in mean field spin glass models

- Physics
- 1992

We present two rigorous results on the Sherrington-Kirkpatrick mean field model for spin glasses, proven by elementary methods, based on properties of fluctuations, with respect to the external…

### Kac limit for finite-range spin glasses.

- PhysicsPhysical review letters
- 2004

It is shown that the infinite-volume free energy of the system converges to that of the Sherrington-Kirkpatrick one, in the Kac limit gamma-->0.1, which could be a first step toward an expansion around mean-field theory, for spin glass systems.

### High temperature regime for a multidimensional Sherrington–Kirkpatrick model of spin glass

- Physics
- 1998

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…

### Central Limit Theorems for the Energy Density in the Sherrington-Kirkpatrick Model

- Mathematics, Physics
- 2009

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…

### Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model

- Physics
- 2015

We consider the fluctuations of the free energy for the 2-spin spherical Sherrington–Kirkpatrick model with no magnetic field. We show that the law of the fluctuations converges to the Gaussian…

### Fluctuations of the Free Energy of the Spherical Sherrington–Kirkpatrick Model with Ferromagnetic Interaction

- Mathematics, Physics
- 2016

We consider a spherical spin system with pure 2-spin spherical Sherrington–Kirkpatrick Hamiltonian with ferromagnetic Curie–Weiss interaction. The system shows a two-dimensional phase transition with…

### The Thermodynamic Limit in Mean Field Spin Glass Models

- Mathematics
- 2002

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…

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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 log Av(Z
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