Precursor phenomena in frustrated systems

TL;DR

This paper investigates precursor phenomena in frustrated systems, linking them to Griffiths and Potts transitions, and clarifies their origins in disorder and frustration through Monte Carlo simulations.

Contribution

It provides a unified interpretation of precursor phenomena in frustrated systems, connecting disorder and frustration to Griffiths and Potts transitions.

Findings

Precursor phenomena are related to Griffiths and Potts transitions.

Disorder induces Griffiths transition, frustration induces Potts transition.

Results apply to both disordered and fully frustrated models.

Abstract

To understand the origin of the dynamical transition, between high temperature exponential relaxation and low temperature nonexponential relaxation, that occurs well above the static transition in glassy systems, a frustrated spin model, with and without disorder, is considered. The model has two phase transitions, the lower being a standard spin glass transition (in presence of disorder) or fully frustrated Ising (in absence of disorder), and the higher being a Potts transition. Monte Carlo results clarify that in the model with (or without) disorder the precursor phenomena are related to the Griffiths (or Potts) transition. The Griffiths transition is a vanishing transition which occurs above the Potts transition and is present only when disorder is present, while the Potts transition which signals the effect due to frustration is always present. These results suggest that precursor phenomena in frustrated systems are due either to disorder and/or to frustration, giving a consistent interpretation also for the limiting cases of Ising spin glass and of Ising fully frustrated model, where also the Potts transition is vanishing. This interpretation could play a relevant role in glassy systems beyond the spin systems case.