Two-dimensional anisotropic KPZ growth and limit shapes
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. 6...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
IOP Publishing
2019
|
| Online Access: | https://hdl.handle.net/1721.1/122939 |
| _version_ | 1826192010370875392 |
|---|---|
| author | Borodin, Alexei Toninelli, Fabio |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Borodin, Alexei Toninelli, Fabio |
| author_sort | Borodin, Alexei |
| collection | MIT |
| description | 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 |
| first_indexed | 2024-09-23T09:04:53Z |
| format | Article |
| id | mit-1721.1/122939 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:04:53Z |
| publishDate | 2019 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1229392022-09-26T10:17:31Z Two-dimensional anisotropic KPZ growth and limit shapes Borodin, Alexei Toninelli, Fabio Massachusetts Institute of Technology. Department of Mathematics 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 France. Agence nationale de la recherche (Grant ANR-15-CE40-0020-03) 2019-11-14T19:37:57Z 2019-11-14T19:37:57Z 2018-08-17 2018-07-05 2019-11-08T13:23:38Z Article http://purl.org/eprint/type/JournalArticle 1742-5468 https://hdl.handle.net/1721.1/122939 Borodin, Alexei and Fabio Toninelli. "Two-dimensional anisotropic KPZ growth and limit shapes." Journal of Statistical Mechanics 2018, 8: 083205 © 2018 IOP Publishing en http://dx.doi.org/10.1088/1742-5468/aad6b4 Journal of Statistical Mechanics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf IOP Publishing arXiv |
| spellingShingle | Borodin, Alexei Toninelli, Fabio Two-dimensional anisotropic KPZ growth and limit shapes |
| title | Two-dimensional anisotropic KPZ growth and limit shapes |
| title_full | Two-dimensional anisotropic KPZ growth and limit shapes |
| title_fullStr | Two-dimensional anisotropic KPZ growth and limit shapes |
| title_full_unstemmed | Two-dimensional anisotropic KPZ growth and limit shapes |
| title_short | Two-dimensional anisotropic KPZ growth and limit shapes |
| title_sort | two dimensional anisotropic kpz growth and limit shapes |
| url | https://hdl.handle.net/1721.1/122939 |
| work_keys_str_mv | AT borodinalexei twodimensionalanisotropickpzgrowthandlimitshapes AT toninellifabio twodimensionalanisotropickpzgrowthandlimitshapes |