Dynamical Phase Transition in Kinetically Constrained Models with Energy-Activity Double-Bias Trajectory Ensemble

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• Kinetically constrained models (KCMs) are crucial for understanding complex dynamics, particularly in systems exhibiting slow relaxation.
• Dynamical phase transitions (DPTs) represent abrupt changes in system behavior driven by kinetic factors, distinct from equilibrium phase transitions.
• Previous studies on KCMs like Fredrickson-Andersen and East models have established their importance but require advanced techniques to fully map their phase spaces.

Purpose of the Study:

• To investigate the nature of dynamical phase transitions in the 1D Fredrickson-Andersen and East models.
• To explore the influence of a novel double-bias ensemble approach on these transitions.
• To map the phase diagrams in (s, g, T) space and analyze temperature-dependent transitions.

Main Methods:

• Utilized a recently developed s,g double-bias ensemble approach, biasing dynamical activity (s) and trajectory energy (g).
• Performed extensive numerical simulations to obtain phase diagrams in (s, g, T) space.
• Conducted finite-size scaling analyses using system size and observation time to determine scaling functions and exponents.

Main Results:

• Confirmed that the dynamical phase transitions in both models are first-order.
• Phase diagrams obtained show qualitative agreement with mean-field predictions.
• Demonstrated the possibility of temperature-dependent dynamical phase transitions when both s and g fields are applied simultaneously; strong correlations between trajectory energy and dynamical activity were observed.
• Finite-size scaling analyses yielded model-dependent scaling exponents for susceptibility and fields.

Conclusions:

• The s,g double-bias ensemble approach is effective for studying DPTs in KCMs.
• Both Fredrickson-Andersen and East models exhibit first-order DPTs, with phase diagrams consistent with mean-field theory.
• The study reveals model-dependent scaling behaviors and the potential for temperature-controlled DPTs, offering insights into the complex dynamics of constrained systems.