Direct evidence for weak universality on fractal structures

We provide a direct quantitative evidence that the critical behavior of the Ising model on self-similar lattices depends upon the geometrical features of the underlying structure. Intensive Monte Carlo simulations enable to show that the values of the ratio of exponents γ/ ν depend upon the lacunari...

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Bibliographic Details
Published inPhysica A Vol. 331; no. 1; pp. 1 - 9
Main Authors Monceau, Pascal, Hsiao, Pai-Yi
Format Journal Article
LanguageEnglish
Published Elsevier B.V 2004
Subjects
Cluster Monte Carlo algorithm
Critical slowing down
Fractal
Phase transitions
75.10.Hk
05.45.Df
75.40.Mg
89.75.Da
Fractal
68.35.Rh
Cluster Monte Carlo algorithm
Critical slowing down
Phase transitions
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Summary:We provide a direct quantitative evidence that the critical behavior of the Ising model on self-similar lattices depends upon the geometrical features of the underlying structure. Intensive Monte Carlo simulations enable to show that the values of the ratio of exponents γ/ ν depend upon the lacunarity of the structure, which measures the deviation from the translational symmetry. Finally, the topological character of the scaling corrections when the fractal dimension is smaller than 2 is discussed.
ISSN:0378-4371
1873-2119
DOI:10.1016/j.physa.2003.09.045