Stretched exponentials and tensionless glass in the plaquette Ising model

TL;DR

This study uses Monte Carlo simulations to demonstrate that the autocorrelation function in a 3D plaquette Ising model exhibits stretched-exponential decay in a supercooled liquid phase, suggesting tensionless droplets influence glassy dynamics.

Contribution

It reveals that tensionless droplets can explain the stretched-exponential decay in the autocorrelation function of a plaquette Ising model, challenging traditional droplet models.

Findings

Autocorrelation function decays as a stretched exponential in the supercooled phase.

Ground-state distributions also show stretched-exponential decay.

Domains in the glassy state are tensionless, with energy scaling as l^1.15.

Abstract

Using Monte Carlo simulations we show that the autocorrelation function $C(t)$ in the d=3 Ising model with a plaquette interaction has a stretched-exponential decay in a supercooled liquid phase. Such a decay characterizes also some ground-state probability distributions obtained from the numerically exact counting of up to 10^450 configurations. A related model with a strongly degenerate ground state but lacking glassy features does not exhibit such a decay. Althoug the stretched exponential decay of C(t) in the three-dimensional supercooled liquid is inconsistent with the droplet model, its modification that considers tensionless droplets might explain such a decay. An indication that tensionless droplets might play some role comes from the analysis of low-temperature domains that compose the glassy state. It shows that the energy of a domain of size l scales as l^1.15, hence these domains are indeed tensionless .