Phase Transitions on Sierpinski Fractals
نویسندگان
چکیده
The present paper focuses on the order-disorder transition of an Ising model on a self-similar lattice. We present a numerical study, based on the Monte Carlo method in conjunction with the finite size scaling method, of the critical properties of the Ising model on a two dimensional deterministic fractal lattice of Hausdorff dimension dH = ln 8/ ln 3 = 1.89278926.... We give evidence of the existence of an order-disorder transition at finite temperature at a value βc ≃ 0.675. By comparing lattices of increasing size we obtain numerical estimates of the critical exponents. Finally we check the hyperscaling relation and find indications that the dimension that plays a role in this relation is the Haussdorff dimension.
منابع مشابه
Geometric Modelling of General Sierpinski Fractals using iterated function system in Matlab
Study on properties of general Sierpinski fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. Like other fractals, general Sierpinski fractals are so complicated and irregular that it is hopeless to model them by simply using classical geometry objects. In [22], the authors the geometric modelling of a class of general Sierpinski fractals and their geometric ...
متن کاملSimulation of Sierpinski-type fractals and their geometric constructions in Matlab environment
Study on properties of Sierpinski-type fractals, including dimension, measure, connectedness, Lipschitz equivalence, etc are very interesting. Although there have been some very nice results were obtained, there is still a long way to go to solve all the problems. In order to facilitate understanding of these results and further study, in this paper, we simulate this kind of fractals and their ...
متن کاملGeometric Modelling of a Class of Sierpinski-type Fractals and Their Geometric Constructions
Study on properties of Sierpinski-type fractals, including dimension, measure, Lipschitz equivalence, etc is very interesting. It is well know that studying fractal theory relies on in-depth observation and analysis to topological structures of fractals and their geometric constructions. But most works of simulating fractals are for graphical goal and often done by non-mathematical researchers....
متن کاملA trace theorem for Dirichlet forms on fractals
We consider a trace theorem for self-similar Dirichlet forms on self-similar sets to self-similar subsets. In particular, we characterize the trace of the domains of Dirichlet forms on the Sierpinski gaskets and the Sierpinski carpets to their boundaries, where boundaries mean the triangles and rectangles which confine gaskets and carpets. As an application, we construct diffusion processes on ...
متن کاملSelf-assembly of the discrete Sierpinski carpet and related fractals (Preliminary version)
It is well known that the discrete Sierpinski triangle can be defined as the nonzero residues modulo 2 of Pascal’s triangle, and that from this definition one can easily construct a tileset with which the discrete Sierpinski triangle self-assembles in Winfree’s tile assembly model. In this paper we introduce an infinite class of discrete self-similar fractals that are defined by the residues mo...
متن کامل