Cluster formulation of spin glasses and the frustrated percolation model: statics and dynamics

TL;DR

This paper investigates a frustrated bond percolation model using Monte Carlo dynamics, revealing a percolation transition in the universality class of the q/2-state Potts model and glass-like relaxation behaviors at low temperatures.

Contribution

It introduces a modified Sweeny algorithm for frustrated bond percolation and links the percolation transition to glassy relaxation phenomena.

Findings

Percolation transition matches q/2-state Potts model universality class.

Relaxation functions exhibit two-step decay below the transition temperature.

At low temperatures, relaxation shows long plateaus similar to glass formers.

Abstract

We study the properties of the q-state frustrated bond percolation model by a Monte Carlo "bond flip" dynamics, using an algorithm originally devised by Sweeny and suitably modified to treat the presence of frustration. We analyze the percolation transition of the model, and find that it falls in the universality class of the q/2-state ferromagnetic Potts model. We then investigate the bond flip dynamics of the model, and find that for temperatures lower than the percolation transition Tp the relaxation functions show a two step decay, reminiscent of the relaxation of glass forming liquids. The long time decay (alpha-relaxation) is well fitted for T<Tp by a stretched exponential function, showing that in this model the relevant mechanism for the appearing of stretched exponentials is the percolation transition. At very low temperatures the relaxation functions develop a long plateau, as observed in glass forming liquids.