Non exponential relaxation in fully frustrated models

TL;DR

This paper investigates the dynamical relaxation in the fully frustrated Ising model, revealing stretched exponential behavior linked to percolation transitions, and highlights how frustration alters critical cluster behavior.

Contribution

It demonstrates non-exponential relaxation in a fully frustrated model and shows how frustration affects the universality class of percolation clusters.

Findings

Stretched exponential relaxation occurs below the percolation temperature T_p.

Frustration changes the universality class of the percolation transition.

Critical behavior of clusters is influenced by frustration, deviating from random percolation.

Abstract

We study the dynamical properties of the fully frustrated Ising model. Due to the absence of disorder the model, contrary to spin glass, does not exhibit any Griffiths phase, which has been associated to non-exponential relaxation dynamics. Nevertheless we find numerically that the model exhibits a stretched exponential behavior below a temperature T_p corresponding to the percolation transition of the Kasteleyn-Fortuin clusters. We have also found that the critical behavior of this clusters for a fully frustrated q-state spin model at the percolation threshold is strongly affected by frustration. In fact while in absence of frustration the q=1 limit gives random percolation, in presence of frustration the critical behavior is in the same universality class of the ferromagnetic q=1/2-state Potts model.