The Potts Fully Frustrated model: Thermodynamics, percolation and dynamics in 2 dimensions

TL;DR

This paper investigates a fully frustrated Potts model in 2D, revealing a thermodynamic transition linked to precursor glassy phenomena, and maps this transition to a percolation transition, providing insights into its thermodynamics and dynamics.

Contribution

It introduces a fully frustrated Potts model without disorder, relates its glassy precursor phenomena to a thermodynamic and percolation transition, and generalizes the ferromagnetic Potts transition temperature.

Findings

Identification of a thermodynamic transition related to glassy phenomena.

Mapping of the transition to a percolation transition.

Estimation of dynamic critical exponents for the model.

Abstract

We consider a Potts model diluted by fully frustrated Ising spins. The model corresponds to a fully frustrated Potts model with variables having an integer absolute value and a sign. This model presents precursor phenomena of a glass transition in the high-temperature region. We show that the onset of these phenomena can be related to a thermodynamic transition. Furthermore this transition can be mapped onto a percolation transition. We numerically study the phase diagram in 2 dimensions (2D) for this model with frustration and {\em without} disorder and we compare it to the phase diagram of $i)$ the model with frustration {\em and} disorder and of $ii)$ the ferromagnetic model. Introducing a parameter that connects the three models, we generalize the exact expression of the ferromagnetic Potts transition temperature in 2D to the other cases. Finally, we estimate the dynamic critical exponents related to the Potts order parameter and to the energy.