Mixed-order phase transition of the contact process near multiple junctions

Area of Science:

• Statistical Physics
• Complex Systems
• Phase Transitions

Background:

• The contact process is a fundamental model for studying spreading phenomena and phase transitions.
• Previous studies focused on translationally invariant or single semi-infinite systems, exhibiting continuous transitions.
• The behavior near multiple junctions (M>2) remained less understood, particularly regarding local order parameters.

Purpose of the Study:

• To investigate the phase transition of the contact process near multiple junctions of M semi-infinite chains.
• To analyze the behavior of the local order parameter and temporal correlation length.
• To explain the observed critical phenomena using theoretical models.

Main Methods:

• Monte Carlo simulations were employed to model the contact process.
• Analysis focused on systems with varying numbers of semi-infinite chains (M).
• A scaling theory involving an irrelevant variable was developed to interpret results.

Main Results:

• A discontinuous local order parameter was observed for M>2, contrasting with continuous transitions in M=1 and M=2 systems.
• The temporal correlation length showed algebraic divergence with distinct exponents across the transition.
• An increase in temporal correlation length with M was noted in the inactive phase.

Conclusions:

• The study reveals a novel discontinuous phase transition for M>2, driven by the junction geometry.
• A scaling theory with a dangerous irrelevant variable successfully explains the unusual local critical behavior.
• Quenched disorder can restore a continuous transition, aligning with renormalization group predictions.