Dresden 2009 – wissenschaftliches Programm
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.