Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 3: Complex energy landscapes (addendum to SYEL)

DY 3.6: Talk

Monday, March 22, 2010, 15:15–15:30, H42

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

The free energy landscape of O(n) vector spin glasses is simplified considerably 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.