Nonsimultaneous hierarchy: multifractal analysis

Amritkar, R. E. ; Gupte, Neelima (1990) Nonsimultaneous hierarchy: multifractal analysis Physical Review A, 41 (6). pp. 3081-3089. ISSN 1050-2947

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We define a simple hierarchical model in two dimensions incorporating two independent and nonsimultaneous rescaling procedures in orthogonal directions. The multifractal framework and corresponding thermodynamic formalism necessary for analyzing models of this type are set up using the concept of partial dimensions, and the model is then analyzed. We define an evolution space such that distinct paths in the evolution space correspond to distinct ways of constructing the hierarchy. If we utilize four scale Cantor sets in the construction of our hierarchy the equivalent Hamiltonian corresponds to that due to nearest-neighbor interactions between spins at the sites of a one-dimensional path on a two-dimensional lattice and is path dependent.

Item Type:Article
Source:Copyright of this article belongs to American Physical Society.
ID Code:493
Deposited On:21 Sep 2010 10:33
Last Modified:12 May 2011 05:16

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