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This study links nonequilibrium phase transitions in patchy diffusion-limited aggregation (DLA) to directed percolation (DP). Patchy DP exhibits a phase transition dependent on patch size, consistent with DP universality classes, offering insights into network formation.

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Nonequilibrium phase transitions are crucial in understanding complex systems.
  • Patchy diffusion-limited aggregation (DLA) exhibits unique growth dynamics.
  • Directed percolation (DP) is a fundamental model for phase transitions.

Purpose of the Study:

  • To investigate the link between patchy DLA and directed percolation (DP).
  • To analyze the phase transition behavior of a patchy DP system.
  • To understand the role of patch size in phase transitions.

Main Methods:

  • Analysis of a directed percolation system with patchy particles (patchy DP).
  • Investigating bond connectivity based on patch size (p).
  • Observing phase transitions from single-seed initiation.

Main Results:

  • Patchy DP demonstrates a nonequilibrium phase transition dependent on critical patch size (p_c).
  • Below p_c, the system enters an absorbing state; above p_c, it remains active.
  • The order parameter exponent (β=0.272±0.010) aligns with the DP universality class.
  • The critical patch size in patchy DP (p_c=0.80625±0.00020) differs from DP's critical bond probability (p_c=0.6447).

Conclusions:

  • The intrinsic nature of patchy DP drives phase transitions in patchy DLA.
  • Patch size probability is not equivalent to bond probability in DP.
  • Provides insights into the formation of extended networks, such as virus capsids.