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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Networks

Background:

  • The Ising model is a fundamental tool for studying magnetism and phase transitions.
  • Small-world networks exhibit unique topological properties, bridging regular and random networks.
  • Competing dynamics introduce non-equilibrium features, enriching system behavior.

Purpose of the Study:

  • Investigate the phase diagram of the 2D Ising model with competing dynamics on an additive small-world network (A-SWN).
  • Analyze the impact of network connectivity (parameter p) on thermodynamic properties and phase transitions.
  • Determine the critical exponents and universality classes for this system.

Main Methods:

  • Utilized Monte Carlo simulations to model the system dynamics.
  • Calculated thermodynamic quantities: total and staggered magnetizations, susceptibility, and Binder cumulant.
  • Performed finite-size scaling analysis to extract critical exponents.

Main Results:

  • Constructed the phase diagram in the temperature (T) versus dynamics probability (q) plane.
  • Identified two continuous phase transition lines for each network parameter p.
  • Observed changes in phase diagram topology and distinct universality classes as p increased.

Conclusions:

  • The A-SWN structure significantly alters the phase transition behavior compared to regular lattices.
  • The competing dynamics and network topology together define the system's critical properties.
  • This model provides insights into non-equilibrium statistical mechanics on complex networks.