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History-dependent percolation in two dimensions.

Minghui Hu1, Yanan Sun1, Dali Wang1

  • 1Department of Physics, Anhui Normal University, Wuhu, Anhui 241000, China.

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Summary
This summary is machine-generated.

History-dependent percolation in 2D transitions to standard universality for finite generations. However, at infinite generations, it exhibits a novel phase transition outside standard universality, showing a crossover phenomenon.

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Area of Science:

  • Statistical physics
  • Complex systems

Background:

  • Percolation theory describes the formation of clusters in random systems.
  • History-dependent percolation introduces temporal evolution to standard models.
  • Understanding phase transitions in evolving systems is crucial.

Purpose of the Study:

  • To investigate the phase transitions of history-dependent percolation in two dimensions.
  • To determine the universality class for finite and infinite generations.
  • To analyze the crossover phenomenon between different universality classes.

Main Methods:

  • Extensive computer simulations on periodic square lattices.
  • Finite-size scaling analysis to identify phase transitions.
  • Calculation of critical exponents and fractal dimensions.

Main Results:

  • For finite generations, the model belongs to the standard 2D percolation universality class.
  • At infinite generations, a distinct phase transition occurs, falling outside standard universality.
  • The correlation-length exponent and fractal dimension differ significantly from standard 2D percolation at infinite generations.
  • A crossover phenomenon is observed between finite and infinite generation universalities.

Conclusions:

  • History-dependent percolation in 2D exhibits rich phase transition behavior.
  • The infinite-generation limit represents a novel universality class.
  • The crossover phenomenon highlights the impact of generational evolution on system properties.