Effect of diffusion in one-dimensional discontinuous absorbing phase transitions.

Area of Science:

• Statistical Physics
• Complex Systems
• Phase Transitions

Background:

• Diffusion significantly impacts continuous absorbing phase transitions.
• The effect of diffusion on discontinuous absorbing phase transitions is less understood.
• The long-range contact process (σ-CP) is a simple 1D model exhibiting discontinuous absorbing phase transitions.

Purpose of the Study:

• To investigate the influence of diffusion on discontinuous absorbing phase transitions.
• To analyze the simplest one-dimensional model with discontinuous absorbing phase transitions, the long-range contact process (σ-CP).
• To understand how diffusion affects the transition dynamics and universality class.

Main Methods:

• Numerical simulations were employed to study the model.
• Mean-field calculations were performed to analyze the system's behavior.
• The study focused on the long-range contact process (σ-CP) with varying diffusion strengths and control parameters (a, σ).

Main Results:

• Three distinct regimes were identified based on the control parameter σ.
• For low and high σ values, the transition remains discontinuous or continuous, respectively, irrespective of diffusion.
• In an intermediate range of σ, diffusion suppresses phase coexistence, inducing a continuous transition within the directed percolation universality class.

Conclusions:

• Diffusion plays a crucial role in determining the nature of phase transitions in the σ-CP model.
• The model exhibits a transition from discontinuous to continuous behavior influenced by diffusion in specific parameter ranges.
• The findings contribute to understanding diffusion's impact on discontinuous phase transitions and their universality classes.