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This study investigates the Manna universality class using a new characteristic length measurement. Results in higher dimensions are consistent, but 1D Manna sandpile models show anomalies with natural initial states, suggesting a distinct universality class.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Computational Physics

Background:

  • The universality class of the Manna model, particularly in one dimension, has been a subject of debate.
  • Previous work suggested the Manna model belongs to the directed percolation (DP) universality class, challenging the existence of an independent Manna universality class.

Purpose of the Study:

  • To apply a novel method for measuring characteristic lengths to models within the Manna universality class.
  • To re-evaluate the universality of the Manna sandpile and conserved lattice gas models in various dimensions.
  • To clarify the Manna model's universality class, especially in one dimension, by addressing discrepancies in previous studies.

Main Methods:

  • Application of a recently developed method for measuring characteristic lengths.
  • Monte Carlo simulations of the stochastic Manna sandpile model in 1, 2, and 3 dimensions.
  • Monte Carlo simulations of the conserved lattice gas model in 3 dimensions.
  • Utilizing both natural initial states (NISs) and uniform initial states (UISs) for simulations.

Main Results:

  • In 2D and 3D, results for the characteristic length R(t) were consistent across both NISs and UISs, aligning with theoretical expectations at the critical point.
  • In 1D, simulations using NISs exhibited anomalous behavior, indicating potential issues with homogenization and finite-size effects in prior studies.
  • Simulations using UISs in 1D showed power-law behavior, with estimated critical exponents diverging from those of the DP universality class.

Conclusions:

  • The findings suggest that the Manna model, particularly in one dimension with NISs, may not belong to the directed percolation universality class.
  • The study provides evidence supporting the existence of an independent Manna universality class, especially when considering appropriate initial states and simulation parameters.
  • The applied characteristic length measurement method proves effective in distinguishing universality classes and highlights the importance of initial state preparation in complex system simulations.