First-order phase transition with a logarithmic singularity in a model with absorbing states

Area of Science:

• Statistical Physics
• Complex Systems

Background:

• A previously studied stochastic lattice model exhibited a discontinuous transition to absorbing states.
• This transition showed an apparent power-law singularity, suggesting a mix of first- and second-order phase transition features.

Purpose of the Study:

• To re-evaluate the nature of the phase transition singularity in the stochastic lattice model.
• To generalize the model to access second-order phase transitions.
• To determine the universality class of the accessible second-order phase transition.

Main Methods:

• Analysis of a stochastic lattice model.
• Mathematical investigation of model definitions and singularities.
• Generalization of the stochastic lattice model.

Main Results:

• The apparent power-law singularity was identified as an artifact of the model's product definition.
• A logarithmic singularity was found at the transition point.
• A generalized model allows access to a second-order phase transition.

Conclusions:

• The original model's transition is characterized by a logarithmic singularity.
• The generalized model's second-order phase transition aligns with the directed percolation universality class.