Domain walls and chaos in the disordered SOS model
| Autor: | Grégory Schehr, Heiko Rieger, Andreas Karrenbauer, Karsten Schwarz |
|---|---|
| Přispěvatelé: | Theoretische Physik, Universität des Saarlandes [Saarbrücken], Max-Planck-Institut für Informatik (MPII), Max-Planck-Gesellschaft, Ecole Polytechnique Fédérale de Lausanne (EPFL), Laboratoire de Physique Théorique d'Orsay [Orsay] (LPT), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2009 |
| Předmět: |
Statistics and Probability
Length scale disordered systems (theory) FOS: Physical sciences 01 natural sciences Fractal dimension 010305 fluids & plasmas Flux Lines Spin-Glass 0103 physical sciences Sensitivity (control systems) [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] 010306 general physics Condensed Matter - Statistical Mechanics Physics Ii Superconductors interfaces in random media (theory) Statistical Mechanics (cond-mat.stat-mech) Mathematical analysis Zero (complex analysis) Systems Ground-State Properties Statistical and Nonlinear Physics Lattices Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks Dynamics Arbitrarily large Phase Domain (ring theory) Statistics Probability and Uncertainty 2 Dimensions ddc:004 Ground state Substrate Energy (signal processing) |
| Zdroj: | Journal of Statistical Mechanics: Theory and Experiment Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2009, pp.P08022 |
| ISSN: | 1742-5468 |
| Popis: | Domain walls, optimal droplets and disorder chaos at zero temperature are studied numerically for the solid-on-solid model on a random substrate. It is shown that the ensemble of random curves represented by the domain walls obeys Schramm's left passage formula with kappa=4 whereas their fractal dimension is d_s=1.25, and therefore is NOT described by "Stochastic-Loewner-Evolution" (SLE). Optimal droplets with a lateral size between L and 2L have the same fractal dimension as domain walls but an energy that saturates at a value of order O(1) for L->infinity such that arbitrarily large excitations exist which cost only a small amount of energy. Finally it is demonstrated that the sensitivity of the ground state to small changes of order delta in the disorder is subtle: beyond a cross-over length scale L_delta ~ 1/delta the correlations of the perturbed ground state with the unperturbed ground state, rescaled by the roughness, are suppressed and approach zero logarithmically. 23 pages, 11 figures |
| Databáze: | OpenAIRE |
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