Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with ferromagnetic interaction

Abstract

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 respect to the temperature and the coupling constant. We compute the limiting distributions of the free energy for all parameters away from the critical values. The zero temperature case corresponds to the well-known phase transition of the largest eigenvalue of a rank 1 spiked random symmetric matrix. As an intermediate step, we establish a central limit theorem for the linear statistics of rank 1 spiked random symmetric matrices.

45 pages, references added

References in corpus (6)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• On the overlap in the multiple spherical SK models
• Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model
• Matrix optimization under random external fields
• The extremal process of critical points of the pure $p$-spin spherical spin glass model
• Fluctuations of the free energy in the mixed $p$-spin models with external field

Cited by in corpus (24)

• Fundamental limits of detection in the spiked Wigner model
• Ferromagnetic to paramagnetic transition in spherical spin glass
• Spherical spin glass model with external field
• Finite Size Corrections and Likelihood Ratio Fluctuations in the Spiked Wigner Model
• Central limit theorem near the critical temperature for the overlap in the 2-spin spherical SK model
• The number of saddles of the spherical $p$-spin model
• Detection limits in the high-dimensional spiked rectangular model
• Free energy fluctuations of the $2$-spin spherical SK model at critical temperature
• Fluctuations Of Linear Spectral Statistics Of Deformed Wigner Matrices
• Critical Fluctuations for the Spherical Sherrington-Kirkpatrick Model in an External Field
• Fluctuation of the free energy of Sherrington-Kirkpatrick model with Curie-Weiss interaction: the paramagnetic regime
• Local Central Limit Theorem for Multi-Group Curie-Weiss Models
• Weak Detection in the Spiked Wigner Model with General Rank
• Weak detection in the spiked Wigner model
• Detection of Signal in the Spiked Rectangular Models
• Spherical Integrals of Sublinear Rank
• Mean Field Spin Glass Models under Weak External Field
• Overlap of a spherical spin glass model with microscopic external field
• Finite-size relaxational dynamics of a spike random matrix spherical model
• Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with heavy-tailed interaction
• Fluctuations of the Stieltjes transform of the empirical spectral distribution of selfadjoint polynomials in Wigner and deterministic diagonal matrices
• Precise Error Rates for Computationally Efficient Testing
• Color symmetry and ferromagnetism in Potts spin glass
• Gaussian fluctuations for linear spectral statistics of deformed Wigner matrices