Berlin 2005 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 40: Statistical Physics (General) I

DY 40.7: Vortrag

Dienstag, 8. März 2005, 11:45–12:00, TU H3010

Test of Replica Theory: Thermodynamics of 2D systems with quenched disorder — •Thorsten Emig — Institut für Theoretische Physik, Universität zu Köln, Zülpicher Str. 77, 50937 Köln

The so-called replica trick is a common tool to study disordered systems like spin glasses or elastic objects in a random potential. It relies on assumptions as, e.g., the analyticity in the replica number, which in general are uncontrolled. Therefore it is important to study sufficient simple but generic model glasses for which the general concepts can be tested.

Here we provide one of the first detailed tests of replica theory. We study a planar lattice of elastic strings pinned by disorder and the random bond dimer model on a square lattice are examined. Whereas the first system can be studied by Replica Bethe ansatz, the latter system is studied numerically by a polynomial algorithm which circumvents slow glassy dynamics. A mapping between the two systems is established which allows for the detailed quantitaive comparison of the replica theory predictions to simulation data. Over a wide range of disorder strength excellent agreement for various thermodynamic quantities is found. Realizations of the studied models include vortex lattices in superconductors, domain walls in incommensurate systems, rough crystal surfaces or frustrated Ising spin systems.

[1] T. Emig and S. Bogner, Phys. Rev. Lett. 90, 185701 (2003). [2] T. Emig and M. Kardar, Nucl. Phys. B 604, 479 (2001).