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.
Cite
@article{arxiv.0912.2959,
title = {Dimer mean-field model for the Ising spin glass},
author = {Yonatan Dubi and Massimiliano Di Ventra},
journal= {arXiv preprint arXiv:0912.2959},
year = {2009}
}