Local Scale-Invariance of the 2+1 dimensional Kardar-Parisi-Zhang model

TL;DR

This study tests local scale-invariance theory against extensive simulations of the 2+1D KPZ surface growth model, finding that logarithmic extensions of LSI better describe the autoresponse function's evolution.

Contribution

It provides the first detailed numerical validation of local scale-invariance, especially its logarithmic extension, in a 2+1 dimensional surface growth model.

Findings

Simple LSI does not fit the data well.

Logarithmic LSI extensions fit the autoresponse function accurately.

Supports the relevance of logarithmic LSI in higher-dimensional growth models.

Abstract

Local Scale-Invariance theory is tested by extensive dynamical simulations of the driven dimer lattice gas model, describing the surface growth of the 2+1 dimensional Kardar-Parisi-Zhang surfaces. Very precise measurements of the universal autoresponse function enabled us to perform nonlinear fitting with the scaling forms, suggested by local scale-invariance (LSI). While the simple LSI ansatz does not seem to work, forms based on logarithmic extension of LSI provide satisfactory description of the full (measured) time evolution of the autoresponse function.