Systems with two symmetric absorbing states: relating the microscopic dynamics with the macroscopic behavior

Area of Science:

• Statistical Physics
• Complex Systems

Background:

• Spin models with symmetric absorbing states are crucial in understanding phase transitions.
• Existing models often lack a unified framework to explain diverse macroscopic behaviors.

Purpose of the Study:

• To propose a general theoretical approach for studying spin models with two symmetric absorbing states.
• To derive a Langevin equation that captures the coarsening dynamics and transition types.

Main Methods:

• Microscopic spin dynamics on a square lattice.
• Derivation of a Langevin equation for magnetization field evolution.
• Mean-field analysis of the derived equation.
• Monte Carlo simulations for validation.

Main Results:

• The macroscopic behavior depends only on the first derivatives of spin-flip probabilities.
• The derived Langevin equation successfully explains coarsening properties.
• Identified three common transition types: generalized voter, Ising, and directed percolation.

Conclusions:

• The proposed general approach provides a unified framework for studying spin models with symmetric absorbing states.
• Theoretical predictions are qualitatively supported by Monte Carlo simulations.
• The study offers insights into the fundamental mechanisms driving phase transitions in complex systems.