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Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder

Simon Bogner·Thorsten Emig·Ahmed Taha·Chen Zeng
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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 2-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, for the first time, a detailed quantitative confirmation of the replica approach and renders the planar line lattice a unique testing ground for concepts in random systems.

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Simon Bogner, Thorsten Emig, Ahmed Taha, Chen Zeng. 2003-09-05. Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder. https://doi.org/10.1103/physrevb.69.104420

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