منابع مشابه
Fractal structure of the six-vertex model
A fractal set which corresponds to the six-vertex model has been obtained and a relationship between the free energy of the six-vertex model and the fractal dimension of the fractal set was established. Notions which correspond to the transfer matrix and the n-equivalence has been found in the area of the fractal geometry. This correspondence can be generalized to the case of the models suitabl...
متن کاملFractal structure of a solvable lattice model
Fractal structure of the six-vertex model is introduced with the use of the IFS (Iterated Function Systems). The fractal dimension satisfies an equation written by the free energy of the six-vertex model. It is pointed out that the transfer matrix method and the n-equivalence relation introduced in lattice theories have also been introduced in the area of fractal geometry. All the results can b...
متن کاملFractal Structure with a Typical Scale
In order to understand characteristics common to distributions which have both fractal and non-fractal scale regions in a unified framework, we introduce a concept of typical scale. We employ a model of 2d gravity modified by the R term as a tool to understand such distributions through the typical scale. This model is obtained by adding an interaction term with a typical scale to a scale invar...
متن کاملHeat kernels and sets with fractal structure
In these notes I will concentrate mainly on heat kernel estimates on ‘pre-fractal graphs’ – for what these are see below. In the final section I will then explain briefly how these estimates can be used to define diffusion processes on some regular true fractal sets. For other (mathematical) surveys of this area see [3], [48], and Kigami’s book [33]. A survey of the physics literature can be fo...
متن کاملFractal Structure of Equipotential Curves on a Continuum Percolation Model
We numerically investigate the electric potential distribution over a twodimensional continuum percolation model between the electrodes. The model consists of overlapped conductive particles on the background with an infinitesimal conductivity. Using the finite difference method, we solve the generalized Laplace equation and show that in the potential distribution, there appear the quasi-equipo...
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ژورنال
عنوان ژورنال: Physical Review D
سال: 2020
ISSN: 2470-0010,2470-0029
DOI: 10.1103/physrevd.101.054022