Potts fully frustrated model: thermodynamics, percolation, and dynamics in two dimensions

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• The study examines a novel Potts model incorporating frustrated Ising spins, creating a fully frustrated Potts model.
• This model exhibits precursor phenomena indicative of a glass transition in high-temperature regimes.

Purpose of the Study:

• To investigate the thermodynamic and percolation transition associated with the precursor phenomena of glass transition.
• To numerically analyze the phase diagram of the frustrated Potts model in 2D.
• To generalize the ferromagnetic Potts transition temperature to include frustration and disorder.

Main Methods:

• Numerical study of the 2D phase diagram for the frustrated Potts model without disorder.
• Comparison with phase diagrams of frustrated disordered Potts models and ferromagnetic models.
• Generalization of the exact expression for the 2D ferromagnetic Potts transition temperature.

Main Results:

• The onset of precursor phenomena is linked to a thermodynamic transition, mappable to a percolation transition.
• The 2D phase diagram for the frustrated model without disorder is numerically characterized.
• A generalized expression for the Potts transition temperature is derived, connecting different model variations.

Conclusions:

• The findings establish a connection between glass transition precursors and fundamental phase transitions (thermodynamic and percolation).
• The study provides a unified framework for understanding transition temperatures across different Potts model variations.
• Dynamic critical exponents related to the Potts order parameter and energy are estimated.