English

Dimer mean-field model for the Ising spin glass

Disordered Systems and Neural Networks 2009-12-16 v1 Statistical Mechanics

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.

Keywords

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}
}
R2 v1 2026-06-21T14:24:12.468Z