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Change in order of phase transitions on fractal lattices

Author

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  • Windus, Alastair Lee
  • Jensen, Henrik Jeldtoft

Abstract

We re-examine a population model which exhibits a continuous absorbing phase transition belonging to directed percolation in 1D and a first-order transition in 2D and above. Studying the model on Sierpinski Carpets of varying fractal dimensions, we examine at what fractal dimension 1≤df≤2, the change in order occurs. As well as commenting on the order of the transitions, we produce estimates for the critical points and, for continuous transitions, some critical exponents.

Suggested Citation

  • Windus, Alastair Lee & Jensen, Henrik Jeldtoft, 2009. "Change in order of phase transitions on fractal lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3107-3112.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:15:p:3107-3112
    DOI: 10.1016/j.physa.2009.04.008
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    Cited by:

    1. Doménech, Antonio, 2009. "A topological phase transition between small-worlds and fractal scaling in urban railway transportation networks?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4658-4668.
    2. Golmankhaneh, Alireza K. & Tunç, Cemil, 2019. "Sumudu transform in fractal calculus," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 386-401.

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