SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 28: Focus Session: Critical Transitions in Society, Economy, and Nature (joint session SOE/DY)

DY 28.1: Topical Talk

Mittwoch, 29. März 2023, 09:30–10:00, ZEU 260

Many universality classes in an interface model restricted to non-negative heights — •Peter Grassberger¹, Deepak Dhar², and Pradeep Mohanty³ — ¹JSC, Forschungszentrum Jülich, D-52425 Jülich, Germany — ²Indian Institute of Science Education and Research, Pune, 411 008, India — ³Indian Institute of Science Education and Research - Kolkata Mohanpur, 741 246, India

We present a simple 1-d stochastic model with two control parameters and a rich zoo of phase transitions. At each (discrete) site x and time t, there is an integer n(x,t) that satisfies a linear interface equation with added random noise. Depending on the control parameters, this noise may or may not satisfy detailed balance, so that the model is – for suitable initial conditions – in the Edwards-Wilkinson (EW) or in the Kardar-Parisi-Zhang (KPZ) universality class. But in contrast to these, there is also a constraint n(x,t) ≥ 0. Points x where n>0 on one side and n=0 on the other are called “fronts". These fronts can be “pushed" or “pulled", depending on the control parameters. For pulled fronts, the lateral spreading is in the directed percolation (DP) universality class, while it is of a novel type for pushed fronts, with yet another novel behavior in between. In the DP case, the activity at each active site can in general be arbitrarily large, in contrast to previous realizations of DP. Finally, we find two different types of transitions when the interface detaches from the line n=0 (with ⟨ n(x,t) ⟩ → const on one side, and → ∞ on the other), again with new universality classes. We also discuss a mapping of this model onto a directed Oslo rice pile model in specially prepared backgrounds.