KPZ models: Height gradient fluctuations and the tilt method

Abstract

When an interface model belonging to the KPZ universality class is tilted with average slope m, its average velocity increases in Λ/2 m2. The coefficient Λ can only be related to the non-linear coefficient λ from the KPZ equation if the mean square of the height gradient also increases in bm2 when the interface is tilted. For the continuous KPZ equation, b = 1 and the relation Λ = λ is achieved. In this work, we study the local fluctuations of the height gradient through an analysis of the values of b. We show that, for one-dimensional discrete KPZ models, 1-b ∼ sγb, where s is the discretization step chosen to calculate the height gradient. The exponent γb that we measure matches the power-law exponent associated with the finite-size corrections of the interface average velocity, i.e. γb = 2(ζ- 1), where ζ is the global roughness exponent. Lastly, we show how, for restricted (unrestricted) growth models, the value of b goes to 1 from below (above) as s increases.