Berlin 2008 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 29: Poster II

DY 29.9: Poster

Thursday, February 28, 2008, 16:00–18:00, Poster C

Scaling limit of groundstate dislocation lines in the solid-on-solid model — •Karsten Schwarz and Heiko Rieger — Theoretische Physik, Universität des Saarlandes, PF 151150, D-66041 Saarbrücken

In some cases, it has already been proven that Schramm-Loewner Evolution (SLE_κ) is the scaling limit of a discrete model, e. g. SLE₂ is the scaling limit of the planar loop-erased random walk.
We study dislocation-lines of the groundstate of the disordered two dimensional solid-on-solid model H= ∑_{⟨ i;j ⟩} (h_i−h_j)² with h_i=d_i+n_i (d_i random offset ∈ [0;1), n_i∈ Z). The main aim of our investigation is to answer the question whether the scaling limit of this discrete model can also be described by SLE_κ. So we simulate such lines on several different simply connected domains and control whether properties of SLE_κ are satisfied. As our model is a frustrated system, it is hard to calculate the groundstate efficiently. So we also describe the used network algorithm.