Growth models on the Bethe lattice

Abstract

I report on an extensive numerical investigation of various discrete growth models describing equilibrium and nonequilibrium interfaces on a substrate of a finite Bethe lattice. An unusual logarithmic scaling behavior is observed for the nonequilibrium models describing the scaling structure of the infinite dimensional limit of the models in the Kardar-Parisi-Zhang (KPZ) class. This gives rise to the classification of different growing processes on the Bethe lattice in terms of logarithmic scaling exponents which depend on both the model and the coordination number of the underlying lattice. The equilibrium growth model also exhibits a logarithmic temporal scaling but with an ordinary power law scaling behavior with respect to the appropriately defined lattice size. The results may imply that no finite upper critical dimension exists for the KPZ equation.

5 pages, 5 figures

References in corpus (5)

• Upper critical dimension of the KPZ equation
• Conformal Invariance of Iso-height Lines in two-dimensional KPZ Surface
• Classification of (2+1)-Dimensional Growing Surfaces Using Schramm-Loewner Evolution
• Scaling of Clusters and Winding Angle Statistics of Iso-height Lines in two-dimensional KPZ Surface
• Explosive percolations on the Bethe Lattice

Cited by in corpus (8)

• Recent advances in percolation theory and its applications
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Roughening transition and universality of single step growth models in (2+1)-dimensions
• Surface growth on treelike lattices and the upper critical dimension of the KPZ class
• Link rewiring with local information--induced hybrid percolation transitions
• Explosive percolation on the Bethe lattice is ordinary
• Discontinuous transition in explosive percolation via local suppression
• Numerical Integration of the KPZ and Related Equations on Networks: The Case of the Cayley Tree