Critical Phenomena and Fractals with Dimensionality Near 1
This work is concerned with the critical properties of Ising models on self similar fractal lattices . Fractal lattices are not translationally invariant, in contrast to the usual integer dimensional lattices. A fractal’s simplest characteristic is its fractal dimensionality, D, which is ordinarily not an integer. (The ε-expansion arguments are predicated upon the existence of lattices that combine non integer dimensionality with translational invariance, but no such lattice has been actually exhibited). Numerous real physical systems, e.g. polymers and critical percolation clusters, are usefully viewed as self similar fractals [1,2].
KeywordsIsing Model Critical Phenomenon Fractal Dimensionality Sierpinski Gasket Sierpinski Carpet
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- 2.H. E. Stanley, R. J. Birgenau, P. J. Reynolds, and J. F. Nicoll, J. Phys. C9, L553 (1976)Google Scholar
- 2a.H. E. Stanley, R. J. Birgenau, P. J. Reynolds, and J. F. Nicoll B. B. Mandelbrot, Ann. Israel Phys. Soc. 2, 226 (1978)Google Scholar
- 2b.H. E. Stanley, R. J. Birgenau, P. J. Reynolds, and J. F. Nicoll B. B. Mandelbrot D. Stauffer, S. Kirkpatrick, Les Houches Summer School on III-Condensed Matter 1978, ed. by R. Balian et al (North Holland, 1979), p. 323.Google Scholar
- 3.Y. Gefen, B. B. Mandelbrot and A. Aharony, to be published.Google Scholar
- 4.See e.g. the papers by R. B. Griffiths and by C. J. Thompson in Phase Transitions and Critical Phenomena, edited by C. Domb and M. S. Green (Academic, New York, 1976) vol. 6, p. 357.Google Scholar