TY - JOUR

T1 - Dimer mean-field model for the Ising spin glass

AU - Dubi, Yonatan

AU - Di Ventra, Massimiliano

PY - 2009/12/15

Y1 - 2009/12/15

N2 - 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.

AB - 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.

UR - http://arxiv.org/abs/0912.2959v1

UR - https://www.mendeley.com/catalogue/3be2cea9-1b4b-31a6-b4ab-2cd9a635a940/

M3 - Article

SP - 1

EP - 5

JO - arXiv

JF - arXiv

SN - 2331-8422

IS - 2

ER -