# An inference problem in a mismatched setting: a spin-glass model with Mattis interaction

@inproceedings{Camilli2021AnIP, title={An inference problem in a mismatched setting: a spin-glass model with Mattis interaction}, author={Francesco Camilli and Pierluigi Contucci and Emanuele Mingione}, year={2021} }

The Wigner spiked model in a mismatched setting is studied with the finite temperature Statistical Mechanics approach through its representation as a Sherrington-Kirkpatrick model with added Mattis interaction. The exact solution of the model with Ising spins is rigorously proved to be given by a variational principle on two order parameters, the Parisi overlap distribution and the Mattis magnetization. The latter is identified by an ordinary variational principle and turns out to concentrate… Expand

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Statistical limits of dictionary learning: random matrix theory and the spectral replica method

- Computer Science, Physics
- ArXiv
- 2021

A novel combination of the replica method from statistical mechanics together with random matrix theory, coined spectral replica method, is introduced to conjecture variational formulas for the mutual information between hidden representations and the noisy data as well as for the overlaps quantifying the optimal reconstruction error. Expand

#### References

SHOWING 1-10 OF 47 REFERENCES

Free energy in the mixed p-spin models with vector spins

- Mathematics, Physics
- 2015

Using the synchronization mechanism developed in the previous work on the Potts spin glass model, arXiv:1512.00370, we obtain the analogue of the Parisi formula for the free energy in the mixed even… Expand

A mechanical approach to mean field spin models

- Physics, Mathematics
- 2008

Inspired by the bridge pioneered by Guerra among statistical mechanics on lattice and analytical mechanics on 1+1 continuous Euclidean space-time, we built a self-consistent method to solve for the… Expand

On the mixed even-spin Sherrington–Kirkpatrick model with ferromagnetic interaction

- Mathematics
- 2011

We study a spin system with both mixed even-spin Sherrington-Kirkpatrick (SK) couplings and Curie-Weiss (CW) interaction. Our main results are: (i) The thermodynamic limit of the free energy is given… Expand

Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model

- Mathematics, Physics
- 2003

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… Expand

The Thermodynamic Limit in Mean Field Spin Glass Models

- Mathematics, Physics
- 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… Expand

About the Almeida-Thouless transition line in the Sherrington-Kirkpatrick mean-field spin glass model

- Physics
- 2002

We consider the Sherrington-Kirkpatrick model and we prove that the quenched free energy per spin is strictly larger than the corresponding replica symmetric approximation, for all values of the… Expand

Spin Glass Computations and Ruelle’s Probability Cascades

- Physics, Mathematics
- 2006

We study the Parisi functional, appearing in the Parisi formula for the pressure of the SK model, as a functional on Ruelle's Probability Cascades (RPC). Computation techniques for the RPC… Expand

Griffiths inequalities for the Gaussian spin glass

- Physics, Mathematics
- 2004

The Griffiths inequalities for Ising spin-glass models with Gaussian randomness of non-vanishing mean are proved using properties of the Gaussian distribution and gauge symmetry of the system. These… Expand

Surface Terms on the Nishimori Line of the Gaussian Edwards-Anderson Model

- Mathematics, Physics
- 2006

For the Edwards-Anderson model we find an integral representation for some surface terms on the Nishimori line. Among the results are expressions for the surface pressure for free and periodic… Expand

Mean field models for spin glasses

- 2012

Translation from physics: ‘Glass’: a material which is hard and inflexible (like a solid) but is not completely ordered or lattice-like in its microscropic structure (thus, unlike a crystal or simple… Expand