“School of Particles And Accelerator”

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Paper   IPM / Particles And Accelerator / 13069
School of Particles and Accelerator
  Title:   Growth models on the Bethe lattice
  Author(s):  Abbas Ali Saberi
  Status:   Published
  Journal: Europhys. Lett.
  No.:  10005
  Vol.:  103
  Year:  2013
  Supported by:  IPM
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

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