2003/09/05 by Simon Bogner, Thorsten Emig, Ahmed Taha +2 · 2 citations
Materials Science · Mathematics · Physics and Astronomy · #Material Dynamics and Properties #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.69.104420
16 pages, 14 figures
arxiv created 2003/09/05 · openalex publication_date 2004/03/22 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.