# Dresden 2009 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe

# DF: Fachverband Dielektrische Festkörper

## DF 9: Glass II

### DF 9.5: Vortrag

### Dienstag, 24. März 2009, 15:20–15:40, WIL B321

**Lower critical dimension of the spherical spin glass** — •Frank Beyer and Martin Weigel — Institut für Physik, KOMET 331, Johannes Gutenberg-Universität Mainz, Staudinger Weg 7, 55099 Mainz, Germany

Considering *O*(*n*) vector spin glasses, a major simplification of the free energy
landscape occurs in the limit of an infinite number of spin components
(*n*→∞), i.e., for the spherical spin glass. This simplification comes about
through the fact that in the limit of a large number of spin components the ground
state of a finite system occupies only a finite-dimensional subspace in spin
space. As a consequence, for each system size there exists a finite, critical number *n*^{∗}
of spin components above which the ground-state energy does not change upon further adding
spin dimensions, such that the system effectively describes a spherical spin glass.
Here, this observation is exploited for investigating the stability of the
ordered phase of the spherical spin glass as a function of the spatial dimension of
the lattice. Using the concept of the defect energy, we numerically determine the stiffness
exponents for lattices of various spatial dimensions *d*=2,3,… and use these
results to estimate the lower critical dimension of the model. The results are
compared to estimates resulting from field-theoretic calulcations.