Abstract
The authors have studied the spectral dimension d48T of an infinite class of fractals. The first member (b=2) of the class is the two-dimensional Sierpinski gasket, while the last member (b= infinity ) appears to be a wedge of the ordinary triangular lattice. By studying the electric resistance of the fractals they have been able to calculate exact values of d for the first 200 members of the class. An analysis of the obtained data reveals that for large b the spectral dimension should approach the upper limit of 2 according to the formula d approximately=2-constant (ln b)beta , where beta is not larger than one. This result implies, among other things, that the scaling exponents of the resistivity and diffusion constant should logarithmically vanish at the fractal-lattice crossover.
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