Universal scaling relation for growth phenomena

Abstract

The Family-Vicsek relation is a seminal universal relation obtained for the global roughness at the interface of two media in the growth process. In this work, we revisit the scaling analysis and, through both analytical and computational means, show that the Family-Vicsek relation can be generalized to a new scaling independent of the size, substrate dimension $d$, and scaling exponents. We use properties of lattice growth models in the Kardar-Parisi-Zhang and Villain-Lai-Das Sarma universality classes for $1\le d\le 3$ to support our claims.

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Cited by in corpus (7)

• The Fluctuation-Dissipation Relations: Growth, Diffusion, and Beyond
• Restoring the fluctuation-dissipation theorem in Kardar-Parisi-Zhang universality class through a new emergent fractal dimension
• Universal scaling of electrostatic effects of a curved counter-electrode on the emitter field enhancement
• A geometrical interpretation of critical exponents
• Fractality in resistive circuits: The Fibonacci resistor networks
• Dynamic scaling and Family-Vicsek universality in $SU(N)$ quantum spin chains
• Scaling, Fractal Dynamics and Critical Exponents: Application in a non-integer dimensional Ising model