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This study explores interacting walkers in a 2D space, linking their movement to a three-state opinion model. It reveals distinct regions and novel distribution forms influenced by noise, impacting phase transitions.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Agent-Based Modeling

Background:

  • Interacting walker systems are typically studied in 1D virtual spaces.
  • Opinion dynamics models often simplify agent interactions and spatial dimensions.

Purpose of the Study:

  • To investigate a 2D interacting walker system governed by a 3-state opinion dynamics model.
  • To analyze the impact of noise on phase transitions and distribution properties.

Main Methods:

  • Simulating a 2D walker system with dynamics based on a fully connected three-state opinion model.
  • Varying a noise parameter to drive continuous phase transitions.
  • Analyzing scaling properties and probability distributions along X and Y axes.

Main Results:

  • Identified three distinct regions based on the noise parameter.
  • Observed non-conventional scaling properties and distributions in the absence of noise.
  • Characterized bivariate and marginal distributions as modified biased Gaussian below the critical point and Gaussian above it.
  • Extracted marginal probability distributions and scaling forms exhibiting power-law behavior.

Conclusions:

  • The noise parameter is crucial for continuous phase transitions in this 2D opinion dynamics walker model.
  • The system exhibits unique statistical properties, deviating from conventional forms, especially without noise.
  • The directed nature of the walk significantly influences marginal distributions and observed scaling exponents.