Test of replica theory: Thermodynamics of two-dimensional model systems with quenched disorder

Simon Bogner, Thorsten Emig, Ahmed Taha, and Chen Zeng
Phys. Rev. B 69, 104420 – Published 22 March 2004
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Abstract

We study the statistics of thermodynamic quantities in two related systems with quenched disorder: A (1+1)-dimensional planar lattice of elastic lines in a random potential and the two-dimensional random bond dimer model. The first system is examined by a replica-symmetric Bethe Ansatz (RBA) while the latter is studied numerically by a polynomial algorithm which circumvents slow glassy dynamics. We establish a mapping of the two models which allows for a detailed comparison of RBA predictions and simulations. Over a wide range of disorder strength, the effective lattice stiffness and cumulants of various thermodynamic quantities in both approaches are found to agree excellently. Our comparison provides a detailed quantitative confirmation of the replica approach and renders the planar line lattice a unique testing ground for concepts in random systems.

  • Received 9 September 2003

DOI:https://doi.org/10.1103/PhysRevB.69.104420

©2004 American Physical Society

Authors & Affiliations

Simon Bogner1, Thorsten Emig1, Ahmed Taha2, and Chen Zeng2

  • 1Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
  • 2Department of Physics, George Washington University, Washington, DC 20052, USA

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Vol. 69, Iss. 10 — 1 March 2004

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