Dresden 2009 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 26: Poster II

DY 26.1: Poster

Donnerstag, 26. März 2009, 16:00–18:00, P1A

Spin Glasses and Eigenvalue-Equations — •Katharina Janzen — Institut für Physik, Carl von Ossietzky Universtität 26111 Oldenburg, Germany

Many disordered systems show a transition to a frozen low-temperature phase. Within the replica formalism for spin glasses this transition is signalled by an instability of the replica-symmetric saddle-point. In this approach the transition to the low temperature phase can be reformulated as an eigenvalue problem.

For systems with Gaussian local fields, and therefore scalar order parameter, the corresponding eigenvalue analysis of the fluctuation matrix was performed by de Almeida and Thouless as early as 1976. In general the local field distribution is non-Gaussian - as for the case of diluted spin glasses - and there are infinitely many order parameters.

Following the replica approach of Monasson, the stability analysis for the more general case can be performed. Using the symmetry of the replica-symmetric fluctuation matrix the eigenvalue problem is reduced by techniques from representation theory of the permutation group and it is shown how generalized AT-lines may be compute