Dimer mean-field model for the Ising spin glass

Abstract

A dimer mean-field model for the Ising spin-glass is presented. Despite its simplicity it captures some of the essential features of the spin-glass physics. The distribution of the single-spin magnetization is determined from a self-consistent integral equation. By solving the self-consistency condition numerically, we find that there are two temperature scales characterizing the glass transition. At the first, higher temperature, the glass order parameter becomes non-vanishing, and at the second, freezing temperature, it saturates to its maximal value. The effect of magnetic field and the existence of the Almeida-Thouless line are discussed. Finally, it is shown that the information compressibility, defined as the derivative of entropy with respect to energy, diverges at the freezing temperature. This indicates a zero internal temperature and true glassy dynamics with diverging relaxation times.