Pair contact process with diffusion: failure of master equation field theory

Area of Science:

• Statistical Physics
• Non-equilibrium Phase Transitions
• Theoretical Physics

Background:

• The pair contact process with diffusion (PCPD) is a model system for studying non-equilibrium phase transitions.
• Understanding critical phenomena in open quantum systems requires appropriate theoretical frameworks.

Purpose of the Study:

• To evaluate the efficacy of a microscopic field theory in capturing the continuous phase transition of the PCPD.
• To investigate the renormalization group (RG) flow and its implications for critical exponents and particle correlations.

Main Methods:

• Derivation of a "microscopic" field theory directly from the master equation.
• Analysis of the renormalization group (RG) flow equations.
• Examination of scaling exponents and particle number fluctuations.

Main Results:

• The microscopic field theory fails to adequately describe the PCPD's continuous nonequilibrium phase transition.
• RG flow equations lack a stable fixed point within the physically accessible parameter region.
• A stable RG fixed point outside the accessible regime predicts contradictions with particle fluctuation positivity.

Conclusions:

• A more coarse-grained effective field theory is necessary to accurately describe the critical properties of the PCPD.
• The limitations of microscopic approaches highlight the complexity of non-equilibrium systems.