Two-dimensional anisotropic KPZ growth and limit shapes
Name
1806.10467.pdf
Description
Submitted version
Size
437.55 KB
Format
Adobe PDF
Checksum (MD5)
08413c9d28f10b9b89afcb31a4cc8d68
Author(s)
Borodin, Alexei
Toninelli, Fabio
Date Issued
August 17, 2018
Journal
Journal of Statistical Mechanics
Publisher
IOP Publishing
Citation
Borodin, Alexei and Fabio Toninelli. "Two-dimensional anisotropic KPZ growth and limit shapes." Journal of Statistical Mechanics 2018, 8: 083205 © 2018 IOP Publishing
Version
Original manuscript
Abstract
A series of recent works focused on two-dimensional (2D) interface growth models in the so-called anisotropic KPZ (AKPZ) universality class, that have a large-scale behavior similar to that of the Edwards-Wilkinson equation. In agreement with the scenario conjectured by Wolf (1991 Phys. Rev. Lett. 67 1783-6), in all known AKPZ examples the function giving the growth velocity as a function of the slope ρ has a Hessian with negative determinant ('AKPZ signature'). While up to now negativity was verified model by model via explicit computations, in this work we show that it actually has a simple geometric origin in the fact that the hydrodynamic PDEs associated to these non-equilibrium growth models preserves the Euler-Lagrange equations determining the macroscopic shapes of certain equilibrium 2D interface models. In the case of growth processes defined via dynamics of dimer models on planar lattices, we further prove that the preservation of the Euler-Lagrange equations is equivalent to harmonicity of with respect to a natural complex structure. Keywords: anisotropic KPZ universality class; growth models; Euler-Lagrange equation; dimer model; complex Burgers equation
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1088/1742-5468/aad6b4
