Random-diluted triangular plaquette model: Study of phase transitions in a kinetically constrained model.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Complex Systems

Background:

• The original triangular plaquette model (TPM) exhibits trivial thermodynamics but glassy dynamics, characteristic of kinetically constrained models.
• Investigating modifications to the TPM is crucial for understanding the emergence of thermodynamic behavior in complex systems.

Purpose of the Study:

• To explore how additional interactions influence the thermodynamic properties of the triangular plaquette model (TPM).
• To analyze the occurrence and nature of phase transitions in generalized TPMs with short-range and long-range interactions.

Main Methods:

• Generalization of the TPM by incorporating additional short-range and long-range interactions.
• Theoretical analysis and argumentation for the existence of thermodynamic phase transitions.
• Application of the Bethe approximation to study the finite-temperature phase diagram of the random-diluted TPM.
• Utilizing cavity equations for exact calculations on random regular graphs.

Main Results:

• The introduction of additional interactions transforms the trivial thermodynamics of the TPM, leading to a thermodynamic phase transition.
• Long-range interactions in the modified TPM result in a glass transition characterized as 'random first-order'.
• The Bethe approximation and random regular graph calculations support the conjectures regarding the phase transitions and thermodynamic properties.

Conclusions:

• Modifying the triangular plaquette model with extra interactions is a viable route to induce thermodynamic phase transitions.
• The study provides evidence for a random first-order glass transition in the long-range interacting TPM.
• The findings highlight the interplay between interactions and thermodynamic behavior in kinetically constrained models.