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