Quadratic replica coupling in the Sherrington-Kirkpatrick mean field spin glass model

@article{Guerra2002QuadraticRC,
  title={Quadratic replica coupling in the Sherrington-Kirkpatrick mean field spin glass model},
  author={Francesco Guerra and Fabio L. Toninelli University of Rome 'La Sapienza' and Infn and R. Scuola normale superiore universitaria di Pisa and Pisa},
  journal={Journal of Mathematical Physics},
  year={2002},
  volume={43},
  pages={3704-3716}
}
We develop a very simple method to study the high temperature, or equivalently high external field, behavior of the Sherrington–Kirkpatrick mean field spin glass model. The basic idea is to couple two different replicas with a quadratic term, trying to push out the two replica overlap from its replica symmetric value. In the case of zero external field, our results reproduce the well known validity of the annealed approximation, up to the known critical value for the temperature. In the case of… 

The replica symmetric region in the Sherrington-Kirkpatrick mean field spin glass model. The Almeida-Thouless line

In previous work, we have developed a simple method to study the behavior of the Sherrington-Kirkpatrick mean field spin glass model for high temperatures, or equivalently for high external fields.

Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

Abstract: By using a simple interpolation argument, in previous work we have proven the existence of the thermodynamic limit, for mean field disordered models, including the Sherrington-Kirkpatrick

Replica Symmetry Breaking in Multi-species Sherrington–Kirkpatrick Model

In the Sherrington–Kirkpatrick (SK) and related mixed p-spin models, there is interest in understanding replica symmetry breaking at low temperatures. For this reason, the so-called AT line proposed

Replica symmetry breaking in mean-field spin glasses through the Hamilton–Jacobi technique

During the last few years, through the combined effort of the insight coming from physical intuition and computer simulation, and the exploitation of rigorous mathematical methods, the main features

Fluctuation Results for Multi-species Sherrington-Kirkpatrick Model in the Replica Symmetric Regime

We study the Replica Symmetric region of general multi-species Sherrington-Kirkpatrick (MSK) Model and answer some of the questions raised in Ann. Probab. 43 (2015), no. 6, 3494– 3513, where the

The High Temperature Region of the Viana–Bray Diluted Spin Glass Model

In this paper, we study the high temperature or low connectivity phase of the Viana–Bray model in the absence of magnetic field. This is a diluted version of the well known Sherrington–Kirkpatrick

Interpolating the Sherrington–Kirkpatrick replica trick

Interpolation techniques have become, in the past decades, a powerful approach to describe several properties of spin glasses within a simple mathematical framework. Intrinsically, for their

Central limit theorem for fluctuations in the high temperature region of the Sherrington-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 Ising--Sherrington-Kirpatrick Model in a Magnetic Field at High Temperature

We study a spin system on a large box with both Ising interaction and Sherrington-Kirpatrick couplings, in the presence of an external field. Our results are: (i) existence of the pressure in the

FROM PARISI TO BOLTZMANN. GIBBS POTENTIALS AND HIGH TEMPERATURE EXPANSIONS FOR MEAN FIELD MODELS

We sketch a new framework for the analysis of disordered systems, in particular mean field spin glasses, which is variational in nature and within the formalism of classical thermodynamics. For
...

References

SHOWING 1-10 OF 22 REFERENCES

ABOUT THE OVERLAP DISTRIBUTION IN MEAN FIELD SPIN GLASS MODELS

We continue our presentation of mathematically rigorous results about the Sherrington-Kirkpatrick mean field spin glass model. Here we establish some properties of the distribution of overlaps

Central limit theorem for fluctuations in the high temperature region of the Sherrington-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

Fluctuations and thermodynamic variables in mean field spin glass models

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

Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences

We discuss replica symmetry breaking (RSB) in spin glasses. We update work in this area, from both the analytical and numerical points of view. We give particular attention to the difficulties

Some exact results on the ultrametric overlap distribution in mean field spin glass models (I)

Abstract:The mean field spin glass model is analyzed by a combination of exact methods and a simple Ansatz. The method exploited is general, and can be applied to others disordered mean field models

REPLICA SYMMETRY BREAKING IN SHORT RANGE SPIN GLASSES: A REVIEW OF THE THEORETICAL FOUNDATIONS AND OF THE NUMERICAL EVIDENCE

We discuss Replica Symmetry Breaking (RSB) in Spin Glasses. We present an update about the state of the matter, both from the analytical and from the numerical point of view. We put a particular

Stability of the Sherrington-Kirkpatrick solution of a spin glass model

The stationary point used by Sherrington and Kirkpatrick (1975) in their evaluation of the free energy of a spin glass by the method of steepest descent is examined carefully. It is found that,

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

On the Stability of the Quenched State in Mean-Field Spin-Glass Models

While the Gibbs states of spin-glass models have been noted to have an erratic dependence on temperature, one may expect the mean over the disorder to produce a continuously varying “quenched state.”

The Sherrington-Kirkpatrick model of spin glasses and stochastic calculus: The high temperature case

We study the fluctuations of free energy, energy and entropy in the high temperature regime for the Sherrington-Kirkpatrick model of spin glasses. We introduce here a new dynamical method with the