Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition

Citation
B. Drossel et al., Spin glasses without time-reversal symmetry and the absence of a genuine structural glass transition, PHYS REV E, 62(6), 2000, pp. 7690-7699
Citations number
30
Categorie Soggetti
Physics
Journal title
PHYSICAL REVIEW E
ISSN journal
1063651X → ACNP
Volume
62
Issue
6
Year of publication
2000
Part
A
Pages
7690 - 7699
Database
ISI
SICI code
1063-651X(200012)62:6<7690:SGWTSA>2.0.ZU;2-E
Abstract
We study the three-spin model and the Ising spin glass in a held using the Migdal-Kadanoff approximation. The flows of the couplings and fields indica te no phase transition, but they show even for the three-spin model a slow crossover to the asymptotic high-temperature behavior for large values of t he coupling. We have also evaluated a quantity that is a measure of the deg ree of non-self-averaging, and we found that it can become large for certai n ranges of the parameters and the system sizes. For a spin glass in a fiel d the maximum of non-self-averaging follows a line for given system size th at resembles the de Almeida-Thouless Line. We conclude that non-self-averag ing found in Monte Carlo simulations cannot be taken as evidence for the ex istence of a low-temperature phase with replica symmetry breaking. Models s imilar to the three-spin model have been extensively discussed in order to provide a description of structural glasses. Their theory at mean-field lev el resembles the mode-coupling theory of real glasses. At that level the ap proach via one-step replica symmetry breaking predicts two transitions, the first transition being dynamic and the second thermodynamic. Our results s uggest that in real finite-dimensional glasses there will be no genuine tra nsitions at all, but that some features of mean-field theory could still pr ovide some useful insights.