The ground state energy of the mean field spin glass model

Flora Koukiou (1)

1 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation

From the study of a functional equation of Gibbs measures we calculate the limiting free energy of the Sherrington-Kirkpatrick spin glass model at a particular value of (low) temperature. This implies the following lower bound for the ground state energy $\epsilon_0$ \[\epsilon_0\geq -0.7833\cdots,\] close to the replica symmetry breaking and numerical simulations values.

Mots clés: Gibbs measures; fixed point; large deviations; free energy; mean field spin glass models; ground state energy; Sherrington-Kirkpatrick model

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Flora Koukiou. The ground state energy of the mean field spin glass model. 2008. ⟨hal-00286116v2⟩