Glassy Behavior in the Ferromagnetic Ising Model on a Cayley Tree

R. Melin; J. C. Angles d'Auriac; P. Chandra; B. Doucot

doi:10.1088/0305-4470/29/18/011

Home/Archive/arXiv

arXiv · cond-mat/9509035

Glassy Behavior in the Ferromagnetic Ising Model on a Cayley Tree

R. Melin·J. C. Angles d'Auriac·P. Chandra·B. Doucot

View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a detailed study of the nearest-neighbor ferromagnetic Ising model on a Cayley tree. In the limit of zero field, the system displays glassy behavior below a crossover temperature, $T_g$, that scales inversely with the logarithm of the number of generations; thus $T_g$ is inversely proportional to the logarithm of the logarithm of the number of sites. Non-Gaussian magnetization distributions are observed for $T < T_g$, reminiscent of that associated with the central spin of the Edwards-Anderson model on the same tree; furthermore a dynamical study indicates metastability, long relaxation times and ageing consistent with the development of glassy behavior for a finite but macroscopic number of sites.

Explore related subjects

cond-mat

Keep this discovery

BibTeX RIS

R. Melin, J. C. Angles d'Auriac, P. Chandra, B. Doucot. 1995-09-07. Glassy Behavior in the Ferromagnetic Ising Model on a Cayley Tree. https://doi.org/10.1088/0305-4470%2F29%2F18%2F011

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2015

Spectral Representation for the Effective Macroscopic Response of a Polycrystal: Application to Third-Order Nonlinear Susceptibility

Erratum: In our paper, we show that the spectral representation for isotropic two-component composites also applies to uniaxial polycrystals. We have learned that this result was, in fact, first conjectured by G.W. Milton. While our derivation is more detailed, our result for the spectral function is the same as Milton's. We very much regret not having been aware of this work at the time of writing our paper. Original abstract: We extend the spectral theory used for the calculation of the effective linear response functions of composites to the case of a polycrystalline material with uniaxially anisotropic microscopic symmetry. As an application, we combine these results with a nonlinear decoupling approximation as modified by Ma et al., to calculate the third-order nonlinear optical susceptibility of a uniaxial polycrystal, assuming that the effective dielectric function of the polycrystal can be calculated within the effective-medium approximation.

cond-mat↗

arXiv2014

Towards quantum well hot hole lasers

It should be possible to improve hot-hole laser performance by moving from bulk materials to a quantum well structure. The extra design parameters enable us to alter the band structure by changing the crystal orientation of the growth direction; to use the well width to shift the subband offsets, enabling the effect of the LO phonon scattering cut-off to be controlled; and to use modulation doping to ensure a high hole concentration to increase the gain without the dopants being present in the gain region. We present the first simulations of THz quantum well hot-hole lasers that can produce inversion and optical gain.

cond-mat↗

arXiv2014

The Hall Effect and ionized impurity scattering in Si$_{(1-x)}$Ge$_x$

Using Monte Carlo simulations, we demonstrate that including ionized impurity scattering in models of Si$_{(1-x)}$Ge$_x$ is vital in order to predict the correct Hall parameters. Our results show good agreement with the experimental data of Joelsson et.al. (JAP, 1997).

cond-mat↗