Spin glasses from vertex models

A. P. Young, Robin B. Stinchcombe

The Edwards and Anderson model for spin glasses is investigated by a decimation rescaling transformation applied to a spin- 1 / 2 Ising model. The technique reproduces the exactly known results for a linear chain and, in particular, predicts ordering to a spin-glass type ground state at T=0. For a two-dimensional square lattice it is shown that approximations which give qualitatively correct results in other situations predict no spin-glass transition at any temperature. A comparison is made with results for spin glasses on a Bethe lattice and with an infinite-range spin-glass model, which has been found to exhibit a transition. It is argued that the difference between infinite-range and short-range models is that the former has entirely extended eigenvectors of the random J ij matrix whereas the latter has at least some localized eigenvectors.

Anonymous

M. A. Contínentino, S. Moss de Oliveira

Recent dynamic experiments on spin glasses, in which contours of constant relaxation time are obtained in the plane of magnetic field versus temperature, are discussed from a renormalization-group point of view. We show that two fixed points control the critical behavior of spin glasses and the critical exponents associated with them can be determined through the dynamic experiments. We give a renormalization-group formulation of the fractal cluster model of spin glasses.

Giorgio Parisi A

P. H. Lundow, Ian A. Campbell

Numerical data on scaling of the normalized Binder cumulant and the normalized correlation length are shown for the Thermodynamic limit regime, first for canonical Ising ferromagnet models and then for a range of Ising spin glass models. A fundamental Renormalization Group Theory rule linking the critical exponents for the two observables is well obeyed in the Ising models, but not for the Ising spin glasses in dimensions three and four. We conclude that there is a violation of a standard Josephson hyperscaling rule in Ising spin glasses.

Heiko Rieger