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

Abstract

We consider the 2-spin spherical Sherrington--Kirkpatrick model without external magnetic field where the interactions between the spins are given as random variables with heavy-tailed distribution. We show that the free energy exhibits a sharp phase transition depending on the location of the largest eigenvalue of the interaction matrix. We also prove the order of the limiting free energy and the limiting distribution of the fluctuation of the free energy for both regimes.

32 pages

References in corpus (6)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Spherical spin glass model with external field
• Thermodynamics of the Lévy spin glass
• Replica theory for Levy spin glasses
• Free energy fluctuations of the $2$-spin spherical SK model at critical temperature
• Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with heavy-tailed interaction

Cited by in corpus (1)

• Fluctuations of the free energy of the spherical Sherrington-Kirkpatrick model with heavy-tailed interaction