The Random-Diluted Triangular Plaquette Model: study of phase transitions in a Kinetically Constrained Model

TL;DR

This paper investigates how adding interactions to the Triangular Plaquette Model induces a thermodynamic phase transition, including a glass transition of the Random First-Order type, supported by Bethe approximation analysis.

Contribution

It introduces the Random-Diluted TPM with long-range interactions and provides theoretical evidence for a phase transition, extending understanding of kinetically constrained models.

Findings

Thermodynamic phase transition emerges with added interactions.

Long-range interactions lead to a glass transition of the Random First-Order type.

Finite temperature phase diagram analyzed via Bethe approximation.

Abstract

We study how the thermodynamic properties of the Triangular Plaquette Model (TPM) are influenced by the addition of extra interactions. The thermodynamics of the original TPM is trivial, while its dynamics is glassy, as usual in Kinetically Constrained Models. As soon as we generalize the model to include additional interactions, a thermodynamic phase transition appears in the system. The additional interactions we consider are either short ranged, forming a regular lattice in the plane, or long ranged of the small-world kind. In the case of long-range interactions we call the new model Random-Diluted TPM. We provide arguments that the model so modified should undergo a thermodynamic phase transition, and that in the long-range case this is a glass transition of the "Random First-Order" kind. Finally, we give support to our conjectures studying the finite temperature phase diagram of the Random-Diluted TPM in the Bethe approximation. This corresponds to the exact calculation on the random regular graph, where free-energy and configurational entropy can be computed by means of the cavity equations.