An Exactly Solved Model of Three Dimensional Surface Growth in the Anisotropic KPZ Regime
M. Praehofer, H. Spohn
TL;DR
This paper presents an exact solution for a 3D surface growth model in the anisotropic KPZ regime, revealing logarithmic height correlations through a novel mapping to free fermions.
Contribution
It generalizes the surface growth model to arbitrary inclination and provides an exact steady-state solution with detailed correlation analysis.
Findings
Exact steady growth velocity characterized as saddle type
Logarithmic height correlations proven mathematically
Mapping to free fermions with chiral boundary conditions
Abstract
We generalize the surface growth model of Gates and Westcott to arbitrary inclination. The exact steady growth velocity is of saddle type with principal curvatures of opposite sign. According to Wolf this implies logarithmic height correlations, which we prove by mapping the steady state of the surface to world lines of free fermions with chiral boundary conditions.
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